Systems and methods for expert systems for underbalanced drilling operations using bayesian decision networks

ABSTRACT

Systems and methods are provided for an underbalanced drilling (UBD) expert system that provides underbalanced drilling recommendations, such as best practices. The UBD expert system may include one or more Bayesian decision network (BDN) model that receive inputs and output recommendations based on Bayesian probability determinations. The BDN models may include: a general UBD BDN model, a flow UBD BDN model, a gaseated (i.e., aerated) UBD BDN model, a foam UBD BDN model, a gas (e.g., air or other gases) UBD BDN model, a mud cap UBD BDN model, an underbalanced liner drilling (UBLD) BDN model, an underbalanced coil tube (UBCT) BDN model, and a snubbing and stripping BDN model.

PRIORITY CLAIM

This application claims priority to U.S. Provisional Patent Application No. 61/722,027 filed on Nov. 2, 2012, entitled “Systems and Methods for Expert Systems for Underbalanced Drilling Operations Using Bayesian Decision Networks,” the disclosure of which is hereby incorporated by reference in its entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to the drilling and extraction of oil, natural gas, and other resources, and more particularly to evaluation and selection of underbalanced drilling systems.

2. Description of the Related Art

Oil, gas, and other natural resources are used for numerous energy and material purposes. The search for extraction of oil, natural gas, and other subterranean resources from the earth may cost significant amounts of time and money. Once a resource is located, drilling systems may be used to access the resources, such as by drilling into various geological formations to access deposits of such resources. The drilling systems rely on numerous components and operational techniques to reduce cost and time and maximize effectiveness. For example, drill strings, drill bits, drilling fluids, and other components may be selected to achieve maximum effectiveness for a formation and other parameters that affect the drilling system. Typically, many years of field experience and laboratory work are used to develop and select the appropriate components and operational practices for a drilling system. However, these techniques may be time-consuming and expensive. Moreover, such techniques may produce inconsistent results and may not incorporate recent changes in practices and opinions regarding the drilling systems.

SUMMARY OF THE INVENTION

Various embodiments of methods and systems for expert systems for determining underbalanced drilling operations using Bayesian decision networks are provided herein. In some embodiments, a system is provided that includes one or more processors and a non-transitory tangible computer-readable memory. The non-transitory tangible computer-readable memory includes an underbalanced drilling expert system executable by the one or more processors and configured to provide one or more underbalanced drilling recommendations based on one or more inputs. The underbalanced drilling expert system includes an underbalanced drilling Bayesian decision network (BDN) model. The underbalanced drilling BDN model includes a first section having a formation indicators uncertainty node configured to receive one or more formation indicators from the one or more inputs, a formation considerations decision node configured to receive one or more formation considerations from the one or more inputs, and a first consequences node dependent on the formation indicators uncertainty node and the formation considerations decision node and configured to output the one or more underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from one or more formation indicators and the one or more formation considerations. The underbalanced BDN model includes a second section having a planning phases uncertainty node configured to receive one or more planning phases from the one or more inputs, a planning phases recommendations decision node configured to receive one or more planning phases recommendations from the one or more inputs, and a second consequences node dependent on the planning phases uncertainty node and the planning phases recommendations decision node and configured to output the one or more underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from one or more planning phases and the one or more planning phases recommendations. Finally, the underbalanced drilling BDN model also includes a third section having a an equipment requirements uncertainty node configured to receive one or more equipment requirements from the one or more inputs, an equipment recommendations decision node configured to receive one or more equipment recommendations from the one or more inputs, and a third consequences node dependent on the equipment requirements uncertainty node and the equipment recommendations decision node and configured to output the one or more underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more equipment requirements and the one or more equipment recommendations.

In some embodiments, a computer-implemented method for an underbalanced drilling expert system having an underbalanced drilling Bayesian decision network (BDN) model is provided. The method includes receiving one or more inputs and providing the one or more nodes of a first section of the underbalanced drilling BDN model. The one or more nodes include a formation indicators uncertainty node and a formation considerations decision node. Additionally, the method further includes determining one or more underbalanced drilling recommendations at a consequences node of the first section of the underbalanced drilling BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs and providing the one or more underbalanced drilling recommendations to a user.

Additionally, in some embodiments, a system having one or more processors and a non-transitory tangible computer-readable memory is provided. The memory the memory includes an underbalanced drilling expert system executable by the one or more processors and configured to provide one or more underbalanced drilling recommendations based on one or more inputs. The underbalanced drilling expert system includes a flow underbalanced drilling Bayesian decision network (BDN) model. The flow underbalanced drilling BDN model includes a first section having a tripping types uncertainty node configured to receive one or more tripping types from the one or more inputs, a permeability level uncertainty node configured to receive one or more permeability levels from the one or more inputs, a tripping options decision node configured to receive one or more tripping options from the one or more inputs, and a first consequences node dependent on the tripping uncertainty node, the permeability level uncertainty node, and the tripping options decision node and configured to output the one or more flow underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more tripping types, the one or more permeability levels, and the one or more tripping options. The flow underbalanced drilling BDN model also includes a second section having a connection types uncertainty node configured to receive one or more connection types from the one or more inputs, a connection options decision node configured to receive one or more connection options from the one or more inputs, and a second consequences node dependent on the connection uncertainty node and the connection options decision node and configured to output the one or more flow underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more connection types and the one or more connection options. Finally, the foam underbalanced drilling BDN model includes a third section having a flow drilling types uncertainty node configured to receive one or more flow drilling types from the one or more inputs, a flow drilling options decision node configured to receive one or more flow drilling options from the one or more inputs, and a third consequences node dependent on the flow drilling uncertainty node and the flow drilling options decision node and configured to output the one or more flow underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more flow drilling types and the one or more flow drilling options.

Further, in some embodiments a computer-implemented method for an underbalanced drilling expert system having a flow underbalanced drilling (UBD) Bayesian decision network (BDN) model is provided. The method includes receiving one or more inputs and providing the one or more inputs to one or more nodes of a first section of the flow underbalanced drilling BDN model. The one or more nodes include a tripping uncertainty node configured to receive one or more tripping types, a permeability level uncertainty node configured to receive one or more permeability levels, and a tripping options decision node a tripping options decision node configured to receive one or more tripping options. The method further includes determining one or more underbalanced drilling recommendations at a consequences node of the first section of the flow underbalanced drilling BDN model by calculating one or more Bayesian probabilities based on the one or more inputs and providing the one or more underbalanced drilling recommendations to a user.

Additionally, in some embodiments a system is provided having one or more processors and a non-transitory tangible computer-readable memory accessible by the one or more processors. The memory includes an underbalanced drilling expert system executable by the one or more processors and configured to provide one or more underbalanced drilling recommendations based on one or more inputs. The underbalanced drilling expert system includes a gaseated underbalanced drilling Bayesian decision network (BDN) model. The gaseated underbalanced drilling BDN model includes a first section having a gas injection process uncertainty node configured to receive one or more gas injection process types from the one or more inputs, a gas injection processes characteristics decision node configured to receive one or more gas injection process characteristics from the one or more inputs, and a first consequences node dependent on the gas injection process uncertainty node and the gas infection processes considerations decision node and configured to output the one or more gaseated underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more gas injection process types and the one or more gas injection process characteristics. The gaseated underbalanced drilling BDN model also includes a second section having a fluid volume limits uncertainty node configured to receive one or more fluid volume limits from the one or more inputs, a fluid volume limits requirements decision node configured to receive one or more fluid volume limits requirements from the one or more inputs, and a second consequences node dependent on the fluid volume limits uncertainty node and the fluid volume limits requirements decision node and configured to output the one or more gaseated underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more fluid volume limits and the one or more fluid volume limits requirements. Additionally, the gaseated underbalanced drilling BDN model includes a third section having a kick type uncertainty node configured to receive one or more kick types from the one or more inputs, a kicks recommendations decision node configured to receive one or more kicks recommendations from the one or more inputs, and a third consequences node dependent on the kick type uncertainty node and the kicks recommendations decision node and configured to output the one or more gaseated underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more kick types and the one or more kicks recommendations. Finally, the gaseated underbalanced drilling BDN model includes a fourth section having an operational considerations uncertainty node configured to receive one or more operational considerations from the one or more inputs, an operational recommendations decision node configured to receive one or more operational recommendations from the one or more inputs, and a fourth consequences node dependent on the operational considerations uncertainty node and the operational recommendations decision node and configured to output the one or more gaseated underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more operational recommendations and the one or more operational recommendations.

In some embodiments, a computer-implemented method for an underbalanced drilling expert system having a gaseated underbalanced drilling Bayesian decision network (BDN) model is provided. The method includes receiving one or more inputs and providing the one or more inputs to one or more nodes of a first section of the gaseated underbalanced drilling (UBD) BDN model. The one or more nodes include a gas injection process uncertainty node configured to receive one or more gas injection process types, and a gas injection processes characteristics decision node configured to receive one or more gas injection process characteristics. Additionally, the method includes determining one or more underbalanced drilling recommendations at a consequences node of the first section of the gaseated UBD BDN model by calculating one or more Bayesian probabilities based on the one or more inputs and providing the one or more underbalanced drilling recommendations to a user.

Moreover, in some embodiments a system is provided having one or more processors and a non-transitory tangible computer-readable memory accessible by the one or more processors. The memory includes an underbalanced drilling expert system executable by the one or more processors and configured to provide one or more underbalanced drilling recommendations based on one or more inputs. The underbalanced drilling expert system includes a foam underbalanced drilling (UBD) Bayesian decision network (BDN) model. The foam underbalanced drilling BDN model includes a first section having a foam systems considerations uncertainty node configured to receive one or more foam systems considerations from the one or more inputs, a foam systems recommendations decision node configured to receive one or more foam systems recommendations from the one or more inputs and a first consequences node dependent on the foam systems considerations uncertainty node and the foam systems recommendations decision node and configured to output the one or more underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more foam systems considerations and the one or more foam systems recommendations. The foam underbalanced drilling BDN model also includes a second section having a foam systems designs uncertainty node configured to receive one or more foam system designs from the one or more inputs, a foam system designs recommendations decision node configured to receive one or more foam system designs recommendations from the one or more inputs, and a second consequences node dependent on the foam systems designs uncertainty node and the foam system designs recommendations decision node and configured to output the one or more underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more foam system designs and the one or more foam system designs recommendations.

In some embodiments, a computer-implemented method for an underbalanced drilling expert system having a foam underbalanced drilling (UBD) Bayesian decision network (BDN) model is provided. The method includes receiving one or more inputs and providing the one or more inputs to one or more nodes of a first section of the foam UBD BDN model. The one or more nodes include a foam systems considerations uncertainty node configured to receive one or more foam systems considerations and a foam systems recommendations decision node configured to receive one or more foam systems recommendations. Additionally, the method includes determining one or more underbalanced drilling recommendations at a consequences node of the first section of the foam UBD BDN model, by calculating one or more Bayesian probabilities based on the one or more inputs and providing the one or more underbalanced drilling recommendations to a user.

Additionally, in some embodiments a system is provided having one or more processors and a non-transitory tangible computer-readable memory accessible by the one or more processors. The memory includes an underbalanced drilling expert system executable by the one or more processors and configured to provide one or more underbalanced drilling recommendations based on one or more inputs. The underbalanced drilling expert system includes a gas underbalanced drilling (UBD) Bayesian decision network (BDN) model. The gas underbalanced drilling BDN model includes a first section having a rotary and hammer drilling uncertainty node configured to receive one or more rotary and hammer drilling types from the one or more inputs, a rotary and hammer drilling recommendations decision node configured to receive one or more rotary and hammer drilling recommendations from the one or more inputs, and a first consequences node dependent on the rotary and hammer drilling uncertainty node and the rotary and hammer drilling recommendations decision node and configured to output the one or more air and gas underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more rotary and hammer drilling types and the one or more rotary and hammer drilling recommendations. The gas underbalanced drilling BDN model includes a second section a gas drilling considerations uncertainty node configured to receive one or more gas drilling considerations from the one or more inputs, a gas drilling considerations recommendations decision node configured to receive gas drilling considerations recommendations from the one or more inputs, and a second consequences node dependent on the gas drilling considerations uncertainty node and the gas drilling considerations recommendations decision node and configured to output the one or more air and gas underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more gas drilling considerations and the one or more gas drilling considerations recommendations. Additionally, the gas underbalanced drilling BDN model includes a third section having a gas drilling operations uncertainty node configured to receive one or more gas drilling operations from the one or more inputs, a gas drilling operations recommendations decision node configured to receive gas drilling operations recommendations from the one or more inputs, and a third consequences node dependent on the gas drilling operations uncertainty node and the gas drilling operations recommendations decision node and configured to output the one or more air and gas underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more gas drilling operations and the one or more gas drilling operations recommendations. Finally, the gas underbalanced drilling BDN model includes a fourth section having a gas drilling rig equipment uncertainty node configured to receive one or more gas drilling rig equipment from the one or more inputs, a gas drilling rig equipment recommendations decision node configured to receive gas drilling rig equipment recommendations from the one or more inputs, and a fourth consequences node dependent on the gas drilling rig equipment uncertainty node and the gas drilling rig equipment recommendations decision node and configured to output the one or more air and gas underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more gas drilling rig equipment and the one or more gas drilling rig equipment recommendations.

Further, in some embodiments a computer-implemented method is provided for an underbalanced drilling expert system having a gas underbalanced drilling (UBD) Bayesian decision network (BDN) model. The method includes receiving one or more inputs and providing the one or more inputs to one or more nodes of a first section of the gas underbalanced drilling BDN model. The one or more nodes include a rotary and hammer drilling uncertainty node and a rotary and hammer recommendations decision node. Additionally, the method includes determining one or more underbalanced drilling recommendations at a consequences node of the first section of the gas underbalanced drilling BDN model, by calculating one or more Bayesian probabilities based on the one or more inputs and providing the one or more underbalanced drilling recommendations to a user.

In some embodiments, a system is provided having one or more processors and a non-transitory tangible computer-readable memory accessible by the one or more processors. The memory includes an underbalanced drilling expert system executable by the one or more processors and configured to provide one or more underbalanced drilling recommendations based on one or more inputs. The underbalanced drilling expert system includes a mud cap underbalanced drilling (UBD) Bayesian decision network (BDN) model. The mud cap underbalanced drilling BDN model includes a first section having a mud cap drilling types uncertainty node configured to receive one or more mud cap drilling types from the one or more inputs, a mud cap drilling types recommendations decision node configured to receive one or more mud cap drilling types recommendations from the one or more inputs, and a first consequences node dependent on the mud cap drilling types uncertainty node and the mud cap drilling types recommendations decision node and configured to output the one or more underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more mud cap drilling types and the one or more mud cap drilling types recommendations.

In some embodiments a computer-implemented method is provided for an underbalanced drilling expert system having a mud cap underbalanced drilling (UBD) Bayesian decision network (BDN) model. The method includes receiving one or more inputs and providing the one or more inputs to one or more nodes of a first section of the mud cap UBD BDN model. The one or more nodes include mud cap drilling types uncertainty node configured to receive one or more mud cap drilling types a mud cap drilling types recommendations decision node configured to receive one or more mud cap drilling types recommendations. The method further includes determining one or more underbalanced drilling recommendations at a consequences node of the first section of the mud cap UBD BDN model by calculating one or more Bayesian probabilities based on the one or more inputs and providing the one or more underbalanced drilling recommendations to a user.

Moreover, in some embodiments a system is provided having one or more processors and a non-transitory tangible computer-readable memory accessible by the one or more processors. The memory includes an underbalanced drilling expert system executable by the one or more processors and configured to provide one or more underbalanced drilling recommendations based on one or more inputs. The underbalanced drilling expert system includes an underbalanced liner drilling (UBLD) Bayesian decision network (BDN) model. The UBLD BDN model includes a first section having a UBLD plans uncertainty node configured to receive one or more UBLD plans from the one or more inputs, a UBLD plans recommendations decision node configured to receive one or more UBLD plans recommendations from the one or more inputs, and a first consequences node dependent on the UBLD planning uncertainty node and the UBLD planning recommendations decision node and configured to output the one or more underbalanced liner drilling recommendations based on one or more Bayesian probabilities calculated from the one or more UBLD plans and the one or more UBLD plans recommendations. The UBLD BDN model also includes a second section having a UBLD solvable problems uncertainty node configured to receive one or more UBLD solvable problems from the one or more inputs, a UBLD advantages decision node configured to receive one or more UBLD advantages from the one or more inputs, and a second consequences node dependent on the UBLD problems uncertainty node and the UBLD advantages decision node and configured to output the one or more underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more UBLD solvable problems and the one or more UBLD advantages. Additionally, the UBLD BDN model includes a third section having a UBLD considerations uncertainty node configured to receive one or more UBLD considerations from the one or more inputs, a UBLD considerations recommendations decision node configured to receive one or more UBLD considerations recommendations from the one or more inputs, and a third consequences node dependent on the UBLD considerations uncertainty node and the UBLD recommendations decision node and configured to output the one or more underbalanced liner drilling recommendations based on one or more Bayesian probabilities calculated from the one or more UBLD considerations and the one or more UBLD considerations recommendations.

In some embodiments a computer-implemented method is provided for an underbalanced drilling expert system having an underbalanced drilling liner (UBLD) Bayesian decision network (BDN) model. The method includes receiving one or more inputs and providing the one or more inputs to one or more nodes of a first section of the UBLD BDN model. The one or more nodes include a UBLD plans uncertainty node configured to receive one or more UBLD plans and a UBLD plans recommendations decision node configured to receive one or more UBLD plans recommendations. The method also includes determining one or more underbalanced drilling recommendations at a consequences node of the first section of the UBLD BDN model by calculating one or more Bayesian probabilities based on the one or more inputs and providing the one or more underbalanced drilling recommendations to a user.

Moreover, in some embodiments a system is provided having one or more processors and a non-transitory tangible computer-readable memory accessible by the one or more processors. The memory includes an underbalanced drilling expert system executable by the one or more processors and configured to provide one or more underbalanced drilling recommendations based on one or more inputs. The underbalanced drilling expert system includes an underbalanced coil tube (UBCT) Bayesian decision network (BDN) model. The UBCT BDN model includes a first section having a UBCT preplanning uncertainty node configured to receive one or more UBCT preplans from the one or more inputs, a UBCT preplanning requirements decision node configured to receive one or more UBCT preplan requirements from the one or more inputs, a first consequences node dependent on the UBCT preplanning uncertainty node and the UBCT preplanning recommendations decision node and configured to output the one or more UBCT drilling requirements based on one or more Bayesian probabilities calculated from the one or more UBCT preplans and the one or more UBCT preplan requirements. The UBCT BDN model also includes a second section having a UBCT considerations uncertainty node configured to receive one or more UBCT considerations from the one or more inputs, a UBCT recommendations decision node configured to receive one or more UBCT recommendations from the one or more inputs, and a second consequences node dependent on the UBCT considerations uncertainty node and the UBCT recommendations decision node and configured to output the one or more underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more UBCT considerations and the one or more UBCT recommendations.

In some embodiments a computer-implemented method is provided for an underbalanced drilling expert system having an underbalanced coil tube (UBCT) Bayesian decision network (BDN) model. The method includes receiving one or more inputs and providing the one or more inputs to one or more nodes of a first section of the UBCT BDN model. The one or more nodes include a UBCT preplanning uncertainty node configured to receive one or more UBCT preplans and a UBCT preplanning requirements decision node configured to receive one or more UBCT preplan requirements. The method also includes determining one or more underbalanced drilling recommendations at a consequences node of the first section of the UBCT BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs and providing the one or more underbalanced drilling recommendations to a user.

Further, in some embodiments another system is provided having one or more processors and a non-transitory tangible computer-readable memory accessible by the one or more processors. The memory includes an underbalanced drilling expert system executable by the one or more processors and configured to provide one or more underbalanced drilling recommendations based on one or more inputs. The underbalanced drilling expert system includes a snubbing and stripping Bayesian decision network (BDN) model. The snubbing and stripping BDN model includes a first section having a snubbing types uncertainty node configured to receive one or more snubbing types from the one or more inputs and a snubbing types recommendations decision node configured to receive one or more snubbing types recommendations from the one or more inputs, and a first consequences node dependent on the snubbing types uncertainty node and the snubbing types recommendations decision node and configured to output the one or more underbalanced recommendations based on one or more Bayesian probabilities calculated from the one or more snubbing types and the one or more snubbing types recommendations. The snubbing and stripping BDN model also includes a second section having a snubbing units uncertainty node configured to receive one or more snubbing units from the one or more inputs, a snubbing units recommendations decision node configured to receive one or more snubbing units recommendations from the one or more inputs, and a second consequences node dependent on the snubbing units uncertainty node and the snubbing units recommendations decision node and configured to output the one or more stripping and snubbing recommendations based on one or more Bayesian probabilities calculated from the one or more snubbing units types and the one or more snubbing units recommendations. Additionally, the snubbing and stripping BDN model includes a third section having a snubbing operations uncertainty node configured to receive one or more snubbing operations from the one or more inputs, a snubbing operations recommendations decision node configured to receive one or more snubbing operations recommendations from the one or more inputs, and a third consequences node dependent on the snubbing operations uncertainty node and the snubbing operations recommendations decision node and configured to output the one or more stripping and snubbing recommendations based on one or more Bayesian probabilities calculated from the one or more snubbing operations and the one or more snubbing operations recommendations. Finally, the snubbing and stripping BDN model also includes a fourth section having a stripping procedures uncertainty node configured to receive one or more stripping procedures from the one or more inputs, a stripping procedures recommendations decision node configured to receive one or more stripping procedures recommendations from the one or more inputs, and a fourth consequences node dependent on the stripping procedures uncertainty node and the stripping procedures recommendations decision node and configured to output the one or more stripping and snubbing recommendations based on one or more Bayesian probabilities calculated from the one or more stripping procedures and the one or more stripping procedures recommendations.

Finally, in some embodiments another computer-implemented method is provided for an underbalanced drilling expert system having a snubbing and stripping Bayesian decision network (BDN) model. The method includes receiving one or more inputs and providing the one or more inputs to one or more nodes of a first section of the snubbing and stripping BDN model. The one or more nodes include snubbing types uncertainty node configured to receive one or more snubbing types and a snubbing types recommendations decision node configured to receive one or more snubbing types recommendations. The method also includes determining one or more underbalanced drilling recommendations at a consequences node of the first section of the snubbing and stripping BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs and providing the one or more underbalanced drilling recommendations to a user.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram that illustrates a system in accordance with an embodiment of the present invention;

FIG. 2 is a schematic diagram of a computer and an underbalanced drilling expert system in accordance with an embodiment of the present invention;

FIGS. 3A-3I are block diagrams of processes of an underbalanced drilling expert system in accordance with an embodiment of the present invention;

FIG. 4 is a schematic diagram of an example of a Bayesian decision network model for the selection of a swelling packer in accordance with an embodiment of the present invention;

FIGS. 5-8 are tables of the probability states associated with the nodes of the Bayesian decision network model of FIG. 4;

FIG. 9 is a table of input utility values assigned to a consequences node of the Bayesian decision network model of FIG. 4;

FIG. 10 is a table of total probability calculations for drilling fluid types of the Bayesian decision network model of FIG. 4;

FIG. 11 is a table of Bayesian probability determinations for the Bayesian decision network model of FIG. 4;

FIG. 12 is a table of consequences based on the Bayesian probability determinations depicted in FIG. 11;

FIG. 13 is a table of expected utilities based on the consequences depicted in FIG. 12;

FIG. 14 is a table of consequences based on the probability states depicted in FIG. 8;

FIG. 15 is a table of expected utilities based on the consequences depicted in FIG. 14;

FIGS. 16A-16I are schematic diagrams that depict a general UBD BDN model and inputs to the general UBD BDN model in accordance with an embodiment of the present invention;

FIG. 17 is a schematic diagram that depicts a selected input to the general UBD BDN model of FIG. 16A;

FIG. 18 is a table that depicts the output from the general UBD BDN model of FIG. 16A;

FIGS. 19A-19H are schematic diagrams that depict a flow UBD BDN model and inputs to the flow UBD BDN model in accordance with an embodiment of the present invention;

FIGS. 20A and 20B are schematic diagrams that depict selected inputs to the flow UBD BDN model of FIG. 19A;

FIG. 21. Is a table that depicts the output from the flow UBD BDN model of FIG. 19A;

FIGS. 22A-22I are schematic diagrams that depict a gaseated UBD BDN model and inputs to the gaseated UBD BDN model in accordance with an embodiment of the present invention;

FIGS. 23A and 23B are schematic diagrams that depict a selected input to and an output from the gaseated UBD BDN model of FIG. 22A;

FIGS. 24A-24E are schematic diagrams that depict a foam UBD BDN model and inputs to the foam UBD BDN model in accordance with an embodiment of the present invention;

FIGS. 25A and 25B are schematic diagrams that depict a selected input to and an output from the foam UBD BDN model of FIG. 24A;

FIGS. 26A-26I are schematic diagrams that depict an air and gas UBD BDN model and inputs to the air and gas UBD BDN model in accordance with an embodiment of the present invention;

FIGS. 27A and 27B are schematic diagrams that depict a selected input to and an output from the air and gas UBD BDN model of FIG. 26A;

FIGS. 28A and 28B are schematic diagrams that depict another selected input to and an output from the air and gas UBD BDN model of FIG. 26A;

FIGS. 29A-29G are schematic diagrams that depict a mud cap UBD BDN model and inputs to the mud cap UBD BDN model in accordance with an embodiment of the present invention;

FIGS. 30A and 30B are schematic diagrams that depict a selected input to and an output from the mud cap UBD BDN model of FIG. 29A;

FIGS. 31A and 31B are schematic diagrams that depict another selected input to and an output from the mud cap UBD BDN model of FIG. 29A;

FIGS. 32A-32G are schematic diagrams that depict a UBLD BDN model and inputs to the UBLD BDN model in accordance with an embodiment of the present invention;

FIGS. 33A and 33B are schematic diagrams that depict a selected input to and an output from the UBLD BDN model of FIG. 32A;

FIGS. 34A and 34B are schematic diagrams that depict another selected input to and an output from the UBLD BDN model of FIG. 32A;

FIGS. 35A-35E are schematic diagrams that depict a UBCTD BDN model and inputs to the UBCTD BDN model in accordance with an embodiment of the present invention;

FIGS. 36A and 36B are schematic diagrams that depict a selected input to and an output from the UBCTD BDN model of FIG. 35A;

FIGS. 37A-37I are schematic diagrams that depict a snubbing and stripping BDN model and inputs to the snubbing and stripping BDN model in accordance with an embodiment of the present invention;

FIGS. 38A and 38B are schematic diagrams that depict a selected input to and an output from the snubbing and stripping BDN model of FIG. 37A;

FIGS. 39A and 39B are schematic diagrams that depict a selected input to and an output from the snubbing and stripping BDN model of FIG. 37A;

FIG. 40 is a block diagram that depicts a process for constructing a BDN model in accordance with an embodiment of the present invention; and

FIG. 41 is a block diagram of a computer in accordance with an embodiment of the present invention.

While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail. The drawings may not be to scale. It should be understood, however, that the drawings and detailed description thereto are not intended to limit the invention to the particular form disclosed, but to the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the present invention as defined by the appended claims.

DETAILED DESCRIPTION

As discussed in more detail below, provided in some embodiments are systems, methods, and computer-readable media for an underbalanced drilling (UBD) expert system based on Bayesian decision network (BDN) models. In some embodiments, the UBD expert system includes a user interface and incorporates probability data based on expert opinions. The UBD expert system may include multiple BDN models, such as a general UBD model, a flow UBD drilling model, a gaseated (i.e., aerated) UBD drilling model, a foam UBD model, a gas (e.g., air or other gases) UBD model, a mud cap UBD model, an underbalanced liner drilling (UBLD) model, an underbalanced coil tube (UBCT) drilling model, and a snubbing and stripping model. Each model may include multiple sections and may receive inputs and provide outputs, such as recommendations, based on the inputs. The inputs to an uncertainty node of a BDN model may include probabilities associated with each input, or a user may select a specific input for the uncertainty node. Based on these inputs, and the inputs to a decision node, a model may put recommendations from a consequences node.

FIG. 1 is a block diagram that illustrates a system 100 in accordance with an embodiment of the present invention. The system 100 includes a formation 102, a well 104, and an underbalanced drilling (UBD) system 106. The system 100 also includes an underbalanced drilling expert system 108 for use with the underbalanced drilling system 106. As described further below, the underbalanced drilling expert system 108 may be implemented on a computer and may include one or more Bayesian decision networks to evaluate inputs and output recommended UBD operations for use with the underbalanced drilling system 106. As will be appreciated, the well 104 may be formed on the formation 102 to provide for extraction of various resources, such as hydrocarbons (e.g., oil and/or natural gas), from the formation 102. In some embodiments, the well 104 is land-based (e.g., a surface system) or subsea (e.g., a subsea system).

The underbalanced drilling system 106 may develop the well 104 by drilling a hole into the formation 102 using a drill bit, e.g., a roller cone bits, drag bits, etc. The underbalanced drilling system 106 may generally include, for example, a wellhead, pipes, bodies, valves, seals and so on that enable drilling of the well 104, provide for regulating pressure in the well 16, and provide for the injection of chemicals into the well 104. As used herein, the term underbalanced drilling refers to a drilling operation in which the wellbore pressure is purposely maintained at a lower pressure than the fluid pressure in the formation 102. Accordingly, the UBD drilling system 106 may include, for example, dry air systems, mist systems, aerated mud systems, gaseated systems, foam systems (e.g., stable foam systems) and other suitable systems. During operation, various UBD-specific scenarios may occur that require adjustments to different parameters of the UDB drilling system 106, such as different equipment, different operations, different tripping, different flow, different connections, different gas injections, different gas and fluid volumes, well kicks, different foams, different air and gas systems, different mud caps, different underbalanced liners, different underbalanced coil tubes, and snubbing and stripping. In some embodiments, the well 104, underbalanced drilling system 106 and other components may include sensors, such as temperature sensors, pressure sensors, and the like, to monitor the drilling process and enable a user to gather information about well conditions.

The underbalanced drilling system 106, well 104, and formation 102 may provide a basis for various inputs 112 to the underbalanced drilling expert system 108. For example, as described below, temperature ranges, the formation 102, and potential hole problems may be provided as inputs 112 to the underbalanced drilling expert system 108. The underbalanced drilling expert system 108 may access an expert data repository 114 that includes expert data, such as probability data used by the underbalanced drilling expert system 108. The expert data may be derived from best practices, expert opinions, research papers, and the like. As described further below, based on the inputs 112, the underbalanced drilling expert system 108 may output recommendations for the underbalanced drilling system 106. For example, the underbalanced drilling expert system 108 may provide the optimal equipment, UBD operations, tripping, connections, flow drilling operations, gas injection processes, air and gas operations, and so on as described further below. Based on these recommendations, different practices may be selected and used in the UBD drilling system 106

FIG. 2 depicts a computer 200 implementing an underbalanced drilling expert system 202 in accordance with an embodiment of the present invention. As shown in FIG. 2, a user 204 may interact with the computer 200 and the underbalanced drilling expert system 202. In some embodiments, as shown in FIG. 2, the underbalanced drilling expert system 202 may be implemented in a single computer 200. However, in other embodiments, the underbalanced drilling expert system 202 may be implemented on multiple computers in communication with each other over a network. Such embodiments may include, for example, a client/server arrangement of computer, a peer-to-peer arrangement of computers, or any other suitable arrangement that enables execution of the underbalanced drilling expert system 202. In some embodiments, the underbalanced drilling expert system 202 may implemented as a computer program stored on a memory of the computer 200 and executed by a process of the computer 200.

In some embodiments, the underbalanced drilling expert system 202 may include a user interface 206 and an expert data repository 208. The user interface 206 may be implemented using any suitable elements, such as windows, menus, buttons, web pages, and so on. As described in detail below, the underbalanced drilling expert system 202 may include one or more Bayesian decision network (BDN) models 210 that implemented Bayesian probability logic 212. The BDN models 210 may evaluate selections of inputs and associated probabilities 214 and output a decision 216 from the BDN model. In the embodiments described herein, the BDN model 210 may include nine different BDN models related to UDB drilling: a general approach to UBD model, a flow UBD drilling model, a gaseated (i.e., aerated) UBD drilling model, a foam UBD model, a gas (e.g., air or other gases) UBD model, a mud cap UBD model, an underbalanced liner drilling (UBLD) model, an underbalanced coil tube (UBCT) drilling model, and a snubbing and stripping model. Each model may include multiple sections and is described in further detail below. The UBD expert system 202 may include any one or combination of the models mentioned above. The BDN models 210 may then calculate Bayesian probabilities for the consequences resulting from the selected inputs, and then output recommended operations. For each BDN model, the output may include a table of probabilities for various recommendations, a single recommendation based on the highest Bayesian probability, or expected utility values for each BDN model to enable to user to evaluate and select the operation having the optimal expected utility for the selected inputs.

As described below, a user 204 may use the user interface 206 to enter selections 210 of inputs for the BDN model 210. The associated probabilities for the inputs may be obtained from the expert data repository 208. Based on the inputs 210, a user 204 may receive the outputs 212 from the BDN model 210, such as recommended UBD operations and expected utility values. The output 212 may be provided for viewing in the user interface 206. Further, as explained below, a user may return to the underbalanced drilling expert system 202 to add or change the inputs 214. The BDN model 210 may recalculate the outputs 216 based on the added or changed inputs 214 and the Bayesian probability logic 212. The recalculated outputs 216 may then provide additional or changed recommended underbalanced drilling practices and expected utility values. Here again, the outputs 216 may be provided to the user in the user interface 206. The user 204 may use a single BDN model of the UBD expert system 202, or may use multiple models of the UBD expert system 202, such as two, three, four, five, six, seven, eight, or nine models of the UDB expert system 202.

FIGS. 3A-3I each depict a process corresponding to a BDN model that may be implemented in a UBD expert system in accordance with an embodiment of the present invention. As explained below, a UBD expert system may include any one or combination of the BDN models described below, and thus may executed any one or combination of the processes described in FIGS. 3A-3I. FIG. 3A depicts a process 300 of the operation of a general UBD BDN model of a UBD expert system in accordance with an embodiment of the present invention. Initially, a user interface for an underbalanced drilling expert system may be provided to a user (block 302). From the user interface, various selections of inputs may be received. For example, selections of formation indicators may be received (block 304) by the underbalanced drilling expert system. As explained below, a user may enter a selection of one or more possible formation indicators into the underbalanced drilling expert system. Additionally, selections of UBD planning phases may be received (block 306) by the underbalanced drilling expert system. As explained below, inputs may be provided at any node of a BDN model of the underbalanced drilling expert system. Additionally, in some embodiments, equipment requirements may also be selected and received by the underbalanced drilling expert system (block 308). Finally planned operations a UBD system may be selected and received by the model (block 310). As mentioned above, any one of or combination of these selections may be received. As described below, the BDN model enables a user to enter inputs at any node of the BDN model.

Next, the received selections may be provided as inputs to uncertainty nodes of a general UBD BDN model of the UBD expert system (block 310), and the selected inputs may include associated probability states, as determined from expert data 312. Next, the data from the uncertainly nodes may be combined (i.e., propagated to) a consequence node of the general UBD BDN model based on the expert systems data (block 312). The propagation and determination of consequences is based on the Bayesian logic described below in FIGS. 4-15 and implemented in the UBD BDN model described below and illustrated in FIGS. 16A-161. Next, general recommendations and expected utility values may be calculated by the general UBD BDN model (block 316). Finally, the recommendations and expected utility values may be output in a user interface of the UBD expert system (block 318).

FIG. 3B depicts a process 312 of the operation of flow UBD BDN model of an UBD expert system in accordance with an embodiment of the present invention. The process 312 illustrates inputs and flow recommendations of the underbalanced drilling expert system, as illustrated further below. Initially, a user interface for an underbalanced drilling expert system may be provided to a user (block 313). From the user interface, various selections of inputs may be received. For example, selections of tripping types may be received (block 314) by the underbalanced drilling expert system. As explained below, a user may enter a selection of one or more possible tripping types into the underbalanced drilling expert system. Additionally, selections of connection types may be received (block 315) by the underbalanced drilling expert system. Finally, in some embodiments, flow drilling types may also be selected by a user and received by the underbalanced drilling expert system (block 316). As explained above, any one of or combination of the selections described above may be input by a user and received by the UBD expert system.

Next, the received selections may be provided as inputs to uncertainty nodes of a flow UBD BDN model of the UBD expert system (block 317), and the selected inputs may include associated probability states, as determined from expert data 318. Next, the data from the uncertainly nodes may be combined (i.e., propagated to) a consequence node of the flow UBD BDN model based on the expert systems data (block 319), as based on the Bayesian logic described below in FIGS. 4-15 and implemented in the flow UBD BDN model described below and illustrated in FIGS. 19A-19H. Next, recommendations and expected utility values may be calculated by the BDN model (block 320). Finally, the recommendations and expected utility values may be output in a user interface of the UBD expert system (block 321).

FIG. 3C depicts a process 324 of the operation of another model of an underbalanced drilling expert system in accordance with an embodiment of the present invention. The process 324 illustrates a gaseated (i.e., aerated) UBD BDN model of the underbalanced drilling expert system, as illustrated further below. Again, a user interface for an underbalanced drilling expert system may be provided to a user (block 325). From the user interface, various selections of inputs may be received. For example, selections of a gas injection process may be received (block 326) by the underbalanced drilling expert system. As explained below, a user may enter a selection of one or more gas injection processes into the underbalanced drilling expert system. Additionally, selections of gas and fluid volume limits may be received (block 327) by the underbalanced drilling expert system. In some embodiments, kick types of a UBD system may also be selected by a user and received by the underbalanced drilling expert system (block 328). Finally, a user selection of operational considerations of a gaseated UBD system may also be received by the underbalanced drilling expert system (block 329). Any one of or combination of these selections may be received, as the gaseated UBD BDN model enables a user to enter inputs at any node of the BDN model.

Next, the received selections may be provided as inputs to uncertainty nodes of a gaseated UBD BDN model of the underbalanced drilling expert system (block 330), and the selected inputs may include associated probability states, as determined from expert data 332. Next, the data from the uncertainly nodes may be combined (i.e., propagated to) a consequence node of the gaseated UBD BDN model (block 333) based on the Bayesian logic described below in FIGS. 4-15 and the gaseated UBD BDN model described below and illustrated in FIGS. 22A-22I. Next, recommendations and expected utility values may be calculated by the BDN model (block 334). Finally, the recommended circulation processes and expected utility values may be output in a user interface of the underbalanced drilling expert system (block 335).

FIG. 3D depicts a process 338 of the operation of a UBD expert system and a fourth BDN model in accordance with an embodiment of the present invention. The fourth BDN model may include a foam UBD BDN model. Initially, a user interface for an underbalanced drilling expert system may be provided to a user (block 339). Here again, the user interface may provide for various selections of inputs may be received. For example, selections of foam systems considerations (e.g., challenges and technical limits) may be received (block 340) by the underbalanced drilling expert system. As explained below, a user may enter a selection of one or more considerations into the UBD drilling expert system. Additionally, selections of foam UBD system designs may be received (block 341) by the underbalanced drilling expert system. As explained below, inputs may be provided at any node of a BDN model of the underbalanced drilling expert system and, as mentioned above, any one of or combination of these selections may be received.

Next, the received selections may be provided as inputs to uncertainty nodes of a general UBD BDN model of the UBD expert system (block 342), and the selected inputs may include associated probability states, as determined from expert data 343. Next, the data from the uncertainly nodes may be combined (i.e., propagated to) a consequence node of the general UBD BDN model based on the expert systems data (block 344) based on the Bayesian logic described below in FIGS. 4-15 and implemented in the foam UBD BDN model described below and illustrated in FIGS. 24A-24E. Next, recommendations of foam systems and expected utility values may be calculated by the foam UBD BDN model (block 345). Finally, the recommendations and expected utility values may be output in a user interface of the UBD expert system (block 346).

FIG. 3E depicts a process 348 of the operation of an underbalanced drilling expert system implementing a fifth BDN model in accordance with an embodiment of the present invention. The process 348 depicts use of an air and gas UBD BDN model of the underbalanced drilling expert system, as illustrated further below. Here again, a user interface for an underbalanced drilling expert system may be provided to a user (block 349). From the user interface, various selections of inputs may be received. For example, selections of rotary or hammer drilling may be received (block 350) by the underbalanced drilling expert system. As explained below, a user may enter a selection of one or more rotary or hammer drilling types into the underbalanced drilling expert system. Additionally, selections of considerations (e.g., limits, extremes, challenges, and the like) for air and gas drilling may be received (block 351) by the underbalanced drilling expert system. In some embodiments, gas drilling operation types of a UBD system may also be selected by a user and received by the underbalanced drilling expert system (block 352). Finally, a selection of gas drilling rig equipment for an air and gas UBD system may also be received by the underbalanced drilling expert system (block 353). Any one of or combination of these selections may be received, as the air and gas UBD BDN model enables a user to enter inputs at any node of the BDN model.

Next, the received selections may be provided as inputs to uncertainty nodes of the air and gas UBD BDN model of the underbalanced drilling expert system (block 354), and the selected inputs may include associated probability states, as determined from expert data 355. Next, the data from the uncertainly nodes may be combined (i.e., propagated to) a consequence node of the air and gas UBD BDN model (block 356) based on the Bayesian logic described below in FIGS. 4-15 and the gas BDN model described below and illustrated in FIGS. 26A-26I. Using the Bayesian logic described below, recommendations and expected utility values may then be calculated by the air and gas BDN model (block 357). Finally, recommendations and expected utility values may be output in a user interface of the underbalanced drilling expert system (block 358).

FIG. 3F depicts a process 360 of the operation of a UBD expert system and a sixth BDN model in accordance with an embodiment of the present invention. The process 360 illustrates the inputs to a mud cap BDN model of the underbalanced drilling expert system, as illustrated further below. Initially, a user interface for an underbalanced drilling expert system may be provided to a user (block 361). From the user interface, various selections of inputs may be received. For example, selections of drilling problems may be received (block 362) by the underbalanced drilling expert system. As explained below, a user may enter a selection of one or more possible drilling problems into the underbalanced drilling expert system. Selections of mud cap drilling types may also be received (block 363) by the underbalanced drilling expert system. Finally, in some embodiments, floating mud cap drilling considerations may also be selected by a user and received by the underbalanced drilling expert system (block 364). As explained above, any one of or combination of the selections described above may be input by a user and received by the UBD expert system.

Next, the received selections may be provided as inputs to uncertainty nodes of a flow UBD BDN model of the UBD expert system (block 365), and the selected inputs may include associated probability states, as determined from expert data 366. Next, the data from the uncertainly nodes may be combined (i.e., propagated to) a consequence node of the flow UBD BDN model based on the expert systems data (block 367), as based on the Bayesian logic described below in FIGS. 4-15 and implemented in the mud cap BDN model described below and illustrated in FIG. 29A-29G. Next, recommendations and expected utility values may be calculated by the mud cap BDN model (block 368) and output in a user interface of the UBD expert system (block 369).

FIG. 3G depicts a process 370 of the operation of a UBD expert system and a seventh BDN model in accordance with an embodiment of the present invention. As shown in FIG. 3G, the process 370 illustrates the inputs to an underbalanced liner drilling (UBLD) model of the underbalanced drilling expert system, as illustrated further below. Initially, a user interface for an underbalanced drilling expert system may be provided to a user (block 371). From the user interface, various selections of inputs may be received. For example, selections of UBLD solvable problems may be received (block 372) by the underbalanced drilling expert system. As explained below, a user may enter a selection of one or more problems that may be solved by UBLD drilling into the underbalanced drilling expert system. Additionally, selections of UBLD plans may also be received (block 373) by the underbalanced drilling expert system. Moreover, in some embodiments, UBLD considerations, such as limits and challenges, may also be selected by a user and received by the underbalanced drilling expert system (block 374). As explained above, any one of or combination of the selections described above may be input by a user and received by the UBD expert system.

Next, the received selections may be provided as inputs to uncertainty nodes of a UBLD BDN model of the UBD expert system (block 375), and the selected inputs may include associated probability states, as determined from expert data 376. The data from the uncertainly nodes may then be combined (i.e., propagated to) a consequence node of the UBLD BDN model based on the expert systems data (block 378), as based on the Bayesian logic described below in FIGS. 4-15 and implemented in the UBLD BDN model described below and illustrated in FIGS. 32A-32G. Next, recommendations and expected utility values may be calculated by the UBLD BDN model (block 379) and output in a user interface of the UBD expert system (block 380).

FIG. 3H depicts a process 382 of the operation of a UBD expert system and an eighth BDN model in accordance with an embodiment of the present invention. The eighth BDN model may include an underbalanced coil tube UBCT BDN model. Initially, a user interface for an underbalanced drilling expert system may be provided to a user (block 383). Here again, the user interface may provide for various selections of inputs may be received. For example, selections of pre-planning types of a UBCT system may be received (block 384) by the underbalanced drilling expert system. As explained below, a user may enter a selection of one or more preplans (i.e., preparation plans) for a UBCT drilling system into the UBD drilling expert system. Additionally, selections of UBCT drilling considerations (e.g., challenges) may be received (block 385) by the underbalanced drilling expert system. As explained below, inputs may be provided at any node of a BDN model of the underbalanced drilling expert system and, as mentioned above, any one of or combination of these selections may be received.

Next, the received selections may be provided as inputs to uncertainty nodes of a UBCT BDN model of the UBD expert system (block 386), and the selected inputs may include associated probability states, as determined from expert data 387. Next, the data from the uncertainly nodes may be combined (i.e., propagated to) a consequence node of the UBCT UBD BDN model based on the expert systems data (block 388) based on the Bayesian logic described below in FIGS. 4-15 and implemented in the UBCT UBD BDN model described below and illustrated in FIGS. 35A-35E. Next, recommendations for UBCT systems and expected utility values may be calculated by the foam UBD BDN model (block 389). Finally, the recommendations and expected utility values may be output in a user interface of the UBD expert system (block 390).

Finally, FIG. 3I depicts a process 392 of the operation of a snubbing and stripping BDN model of a UBD expert system in accordance with an embodiment of the present invention. Initially, a user interface for an underbalanced drilling expert system may be provided to a user (block 393). From the user interface, various selections of inputs may be received. For example, selections of snubbing types may be received (block 394) by the underbalanced drilling expert system. As explained below, a user may enter a selection of one or more snubbing types into the underbalanced drilling expert system. Additionally, selections of snubbing units may be received (block 395) by the underbalanced drilling expert system. Additionally, in some embodiments, snubbing operations may also be selected and received by the underbalanced drilling expert system (block 396). Finally, general stripping procedures for a UBD system may be selected and received by the model (block 397). As mentioned above, any one of or combination of these selections may be received, and as described below, the BDN model enables a user to enter inputs at any node of the BDN model.

Next, the received selections may be provided as inputs to uncertainty nodes of a scrubbing and stripping BDN model of the UBD expert system (block 398), and the selected inputs may include associated probability states, as determined from expert data 399. Next, the data from the uncertainly nodes may be combined (i.e., propagated to) a consequence node of the scrubbing and stripping BDN model based on the expert systems data (block 400). The propagation and determination of consequences is based on the Bayesian logic described below in FIGS. 4-15 and implemented in the scrubbing and stripping BDN model described below and illustrated in FIGS. 37A-37I. Next, general recommendations and expected utility values may be calculated by the scrubbing and stripping BDN model (block 401). Finally, the recommendations and expected utility values may be output in a user interface of the UBD expert system (block 402).

FIGS. 4-15 depict an example of a BDN model simulating the decision-making process of the selection of a swelling packer. The model described below in FIGS. 4-15 is illustrative of the application of a Bayesian decision network to the selection of a swelling packer for use in a drilling system. Based on the techniques illustrated in FIGS. 4-15 and described below, various BDN model associated with an UBD expert system, such as that described above in FIGS. 1 and 2 may be implemented. These BDN models are illustrated in detail in FIGS. 16-39 and described below. Thus, the techniques and implementation described in FIGS. 4-15 may be applied to the more detailed BDN models illustrated in FIGS. 16-39.

FIG. 4 depicts a BDN model 400 for the selection of a swelling packer in accordance with an embodiment of the present invention. The BDN model 400 depicted in FIG. 4 includes a swelling packer decision node 402, a treating fluid uncertainty node 404, a drilling fluid type uncertainty node 406, a consequences node 408, and a completion expert system value node 410. As will be appreciated, the selection of a swelling packer may be relevant in the completion of a well to production status. In the illustrated BDN model 400, the various connection lines 412 indicate direct dependencies between the different nodes. Accordingly, the consequences node may be influenced by the inputs to the uncertainty nodes 404 and 406 and the decision node 402. Similarly, the treating fluid uncertainty node 404 may be influenced by the swelling packer decision node 402.

After defining the BDN model 400, the probability states associated with each node may be defined. FIGS. 5-7 depict various tables illustrating the states, such as probability states, associated with each node of the BDN model 400. The probability distributions may be defined based on expert data entered in the BDN model 400. FIG. 5 depicts a table 500 illustrating the states associated with the swelling packer decision node 402. As shown in table 500, the swelling packer decision node 402 may have a first probability state 502 of “water swelling packer” and a second probability state 504 of “oil swelling packer.” Next, FIG. 6 depicts a table 600 illustrating the probability states associated with the treating fluid uncertainty node 404. The probability states associated with the treating fluid uncertainty node 404 are influenced by the dependency on the swelling packer decision node 402. As shown in table 600, the probability states for two treating fluids 602 (“Lactic acid”) and 604 (“HCl acid”) are shown. For example, for a lactic acid treating fluid 602, the probability state for a water swelling packer 606 is 0.9 and the probability state for an oil swelling packer 608 is 0.5. Similarly, for an HCl acid treating fluid 604, the probability state for the water swelling packer 606 is 0.1 and the probability state for the oil swelling packer 608 is 0.5.

FIG. 7 depicts a table 700 illustrating the probability states associated with the drilling fluid type uncertainty node 406. As shown in the BDN model 400 depicted in FIG. 4, the drilling fluid type uncertainty node 406 is influenced by the dependency on the treating fluid uncertainty node 404 and the swelling packer decision node 406. In the table 700, the probably states associated with two drilling fluid types 702 (“Formate drilling fluid”) and 704 (“CaCO₃ drilling fluid”) are depicted for combinations of a water swelling packer 706, an oil swelling packer 708, a lactic acid treating fluid 710, and an HCl acid treating fluid 712. For example, as shown in FIG. 7, for the formate drilling fluid type 702, the probability state for the water swelling packer 706 and lactic acid treating fluid 710 is 0.8 and the probability state for the water swelling packer 706 and HCl acid treating fluid 712 is 0.2. Similarly, for the CaCO₃ drilling fluid type 704, the probability state for the water swelling packer 706 and lactic acid treating fluid 710 is 0.2 and the probability state for the water swelling packer 706 and HCl acid treating fluid 712 is 0.8. In a similar manner, the table 700 of FIG. 7 depicts the probability states for the oil swelling packer 708 and the various combinations of lactic acid treating fluid 710 and the HCl acid treating fluid 712, and the formate drilling fluid type 702 and the CaCO₃ drilling fluid type 704.

FIG. 8 depicts a table 800 illustrating the probability states of the consequences node 408. The consequences node 408 is influenced by its dependency on the swelling packer decision node 402, treating fluid uncertainty node 404, and the drilling fluid type uncertainty node 406. As shown in table 800, the probability states associated with two consequences 802 (“Recommended”) and 804 (“Not recommended”) are depicted for various combinations of a water swelling packer 806 or an oil swelling packer 808, a formate drilling fluid type 810 or a CaCO₃ drilling fluid type 812, and a lactic acid treating fluid 814 or an HCl acid treating fluid 816. For example, for the Recommended consequence 802, the probability state for the combination of water swelling packer 806, the formate drilling fluid 810, and lactic acid treating fluid 814 is 0 and the probability state for the combination of the water swelling packer 806, the formate drilling fluid 810, and HCl acid treating fluid 816 is 1. In another example, as shown in table 800, for the Not recommended consequence 804, the probability state for combination of the water swelling packer 806, the formate drilling fluid 810, and lactic acid treating fluid 814 is 1 and the probability state for the combination of the water swelling packer 806, the formate drilling fluid 810, and HCl acid treating fluid 816 is 0.

In the BDN model 400, the consequences associated with the consequences utility node 408 may be assigned input utility values. FIG. 9 depicts a table 900 illustrating the input utility values assigned to the consequences from the consequences utility node 408. As shown in table 900, a value 902 may be assigned to each consequence of the consequence node 408. For a consequence 904 of Recommended, an input utility value of 1 may be assigned. Similarly, for a consequence 906 of Not Recommended, an input utility value of 0 may be assigned. As described below, after the probability states for the consequences are determined in the BDN model 400, the input utility values assigned to each consequence may be

Using the model and probabilities described above, the functionality of the BDN model 400 will be described. After receiving inputs to the model 400, the model 400 may simulate the uncertainty propagation based on the evidence, e.g., the probability states, at each node, using Bayesian probability determinations. A Bayesian probability may be determined according to Equation 1:

$\begin{matrix} {{p\left( {{hypothesis}{evidence}} \right)} = \left( \frac{{p\left( {{evidence}{hypothesis}} \right)}{p({hypothesis})}}{p({evidence})} \right)} & (1) \end{matrix}$

Where:

p(hypothesis|evidence) is the probability of a hypothesis conditioned upon evidence; p(evidence|hypothesis) is the probability the evidence is plausible based on the hypothesis; p(hypothesis) is the degree of certainty of the hypothesis; and p(evidence) is the degree of certainty of the evidence.

Referring again to the BDN model 400 discussed above, the model 400 illustrates that a selection of drilling fluid affects the treating fluid and the swelling packer, as illustrated by the dependencies in the model 400. First, the total probability for a drilling fluid type may be calculated based on the evidence from the uncertainty nodes by Equation 2:

$\begin{matrix} {\sum\limits_{i = 1}^{m}{{P\left( {BA_{i}} \right)}{P\left( A_{i} \right)}}} & (2) \end{matrix}$

Where:

P(B|A_(i)) is the probability based on B in view of A_(i); P(A_(i)) is the probability of A_(i); and m is the total number of evidence items.

Using Equation 2, the total probability for a drilling fluid type and lactic acid treating fluid may be calculated according to Equation 3:

$\begin{matrix} {\sum\limits_{i = 1}^{m}{{p\left( {{formatedrillingfluid}{lacticacid}_{i}} \right)}{P\left( {lacticacid}_{i} \right)}}} & (3) \end{matrix}$

For example, using the probability data illustrated in FIGS. 6 and 7, the total probability for a formate drilling fluid type may be calculated as the sum of 0.9 (probability for a lactic acid treating fluid and water swelling packer) multiplied by 0.8 (probability for a formate drilling fluid type, lactic acid treating fluid, and water swelling packer) and 0.1 (probability for a lactic acid treating fluid and water swelling packer) multiplied by 0.2 (probability for a lactic acid treating fluid and water swelling packer).

The results of the total probability calculations for drilling fluid types are illustrated in table 1000 depicted in FIG. 10. Table 1000 depicts the total probabilities for various combinations of drilling fluids 1002 (“Formate drilling fluid) and 1004 (“CaCO3 drilling fluid”) and a water swelling packer 1006 and an oil swelling packer 1008. As explained above, the total probabilities at the drilling fluid uncertainty node are dependent on the evidence from the treating fluid uncertainty node and the swelling packer decision node. As shown in table 1000 of FIG. 10, the total probability for a formate drilling fluid 1002 and the water swelling packer 1006 is 0.74, and the total probability for a formate drilling fluid 1002 and the oil swelling packer 1008 is 0.5. Similarly, total probabilities for the CaCO₃ drilling fluid type 1004 are also depicted in table 1000.

Using the total probabilities determined above, the Bayesian probability determination of Equation 1 may be used to calculate the Bayesian probability of a treating fluid used with a specific drilling fluid type and a particular swelling packer. Accordingly, a Bayesian probability may be derived by combining the Bayesian probability of Equation 1 with the total probability calculation of Equation 2, resulting in Equation 4:

$\begin{matrix} {{P\left( {A_{j}B} \right)} = \frac{{p\left( {BA_{j}} \right)}{P\left( A_{j} \right)}}{\sum\limits_{i = 1}^{m}{{P\left( {BA_{i}} \right)}\left( {P\left( A_{i} \right)} \right.}}} & (4) \end{matrix}$

Thus, based on Equation 4, the Bayesian probability determination for a lactic acid treating fluid and a formate drilling fluid type for a water swelling packer may be determined according to Equation 5, using the total probabilities depicted in the table 700 of FIG. 7 and the table 1000 of FIG. 10:

$\begin{matrix} \begin{matrix} {P\left( {{{lacticacid}{formate}} = \left( \frac{{P\left( {{formate}{lacticacid}} \right)}{P({lacticacid})}}{P({formate})} \right)} \right.} \\ {= \frac{0.8 \times 0.9}{0.74}} \\ {= 0.9729} \end{matrix} & (5) \end{matrix}$

As depicted above in FIG. 7, the probability associated with a formate drilling fluid type conditioned on lactic acid treating fluid is 0.8 and the probability of lactic acid for a water swelling packer is 0.9. Additionally, as calculated above in FIG. 10, the total probability associated with a formate drilling fluid and a water swelling packer is 0.74. Using these probabilities, the Bayesian probability for a lactic acid treating fluid and a formate drilling fluid type may be calculated as shown in Equation 5. Similarly, Equation 6 depicts the Bayesian probability determination for an HCl treating fluid and a formate drilling fluid type, as shown below:

$\begin{matrix} \begin{matrix} {P\left( {{{HClacid}{formate}} = \left( \frac{{P\left( {{formate}{HClacid}} \right)}{P({HClacid})}}{P({formate})} \right)} \right.} \\ {= \frac{0.2 \times 0.1}{0.74}} \\ {= 0.0270} \end{matrix} & (6) \end{matrix}$

As noted above, the values for the probabilities depicted in Equation 6 may be obtained from the probability states depicted in tables 600 and 700 of FIGS. 6 and 7 and the total probability calculations depicted in table 1000 of FIG. 10. In a similar manner, Equations 7 and 8 depict the Bayesian probability determinations for a CaCO₃ drilling fluid type:

$\begin{matrix} \begin{matrix} {P\left( {{{lacticacid}{CaCo}_{3}} = \left( \frac{{P\left( {{CaCo}_{3}{lacticacid}} \right)}{P({lacticacid})}}{P\left( {CaCo}_{3} \right)} \right)} \right.} \\ {= \frac{0.2 \times 0.9}{0.26}} \\ {= 0.6923} \end{matrix} & (7) \\ \begin{matrix} {P\left( {{{HClacid}{CaCo}_{3}} = \left( \frac{{P\left( {{CaCo}_{3}{HClacid}} \right)}{P({HClacid})}}{P\left( {CaCo}_{3} \right)} \right)} \right.} \\ {= \frac{0.8 \times 0.1}{0.26}} \\ {= 0.3076} \end{matrix} & (8) \end{matrix}$

The Bayesian probability determinations may also be performed for an oil swelling packer for the various combinations of treating fluid and drilling fluid types. Using the probability states depicted in tables 600 and 700 of FIGS. 6 and 7 and the total probability calculations depicted in table 1000 of FIG. 10, these Bayesian probability determinations are shown below in Equations 9-12:

$\begin{matrix} \begin{matrix} {P\left( {{{lacticacid}{formate}} = \left( \frac{{P\left( {{formate}{lacticacid}} \right)}{P({lacticacid})}}{P({formate})} \right)} \right.} \\ {= \frac{0.8 \times 0.5}{0.5}} \\ {= 0.8} \end{matrix} & (9) \\ \begin{matrix} {P\left( {{{HClacid}{formate}} = \left( \frac{P\left( {{formate}{HClacid}} \right)}{P({formate})} \right)} \right.} \\ {= \frac{0.2 \times 0.5}{0.5}} \\ {= 0.02} \end{matrix} & (10) \\ \begin{matrix} {P\left( {{{lacticacid}{CaCo}_{3}} = \left( \frac{{P\left( {{CaCo}_{3}{lacticacid}} \right)}{P({lacticacid})}}{P\left( {CaCo}_{3} \right)} \right)} \right.} \\ {= \frac{0.8 \times 0.5}{0.5}} \\ {= 0.8} \end{matrix} & (11) \\ \begin{matrix} {P\left( {{{HClacid}{CaCo}_{3}} = \left( \frac{{P\left( {{CaCo}_{3}{HClacid}} \right)}{P({HClacid})}}{P\left( {CaCo}_{3} \right)} \right)} \right.} \\ {= \frac{0.2 \times 0.5}{0.5}} \\ {= 0.2} \end{matrix} & (12) \end{matrix}$

The results of the calculations shown above in Equations 5-12 are depicted in table 1100 in FIG. 11. Table 1100 depicts the Bayesian probability determinations for treating fluids 1102 (“Lactic acid”) and 1104 (“HCl acid”) and swelling packers 1106 (“water swelling packer”) and 1108 (“oil swelling packer”). The Bayesian probability determinations are shown for both a formate drilling fluid type 1110 and CaCO₃ drilling fluid type 1112.

After determining the Bayesian probabilities described above, the BDN model 400 may be used to select a swelling packer based on the inputs provided to the uncertainty nodes of the model 400. For example, the BDN model 400 may be used with two different interpretations of the output to provide the optimal swelling packer for the inputs provided to the model 400. In one interpretation, the model 400 may receive a user selection of an input for one uncertainty node, and an optimal swelling packer may be determined based on the possible inputs to the other uncertainty node. Thus, as shown table 1100 and FIG. 11, the drilling types 1110 and 1112 may be “Selected by user.” By specifying a type of drilling fluid, the respective Bayesian probability determinations may be read from the table 1100.

FIG. 12 depicts a table 1200 illustrating the consequences for a user selection of a CaCO₃ drilling fluid type based on the Bayesian probability determinations depicted in FIG. 11. For example, if a CaCO₃ drilling fluid type is used to drill a well, the consequences of using a water swelling packer 1202 or an oil swelling packer 1204 are depicted in table 1200. The consequences illustrated in table 1200 may include a “Recommended” consequence 1206 and a “Not Recommended” consequence 1208. Accordingly, for a user selection of a CaCO₃ drilling fluid type, the Bayesian probabilities read from table 1100 for a water swelling packer are 0.6923 for a lactic acid and 0.3076 for an HCl acid treating fluid. Similarly, values for a user selection of a CaCO₃ drilling fluid type and an oil swelling packer are 0.8 and 0.2. As shown in FIG. 12, the Bayesian probability determinations greater than 50% (0.5) may be provided as Recommended consequences 1206 and the Bayesian probability determinations less than 50% (0.5) may be included as Non Recommended consequences 1208.

As mentioned above, table 900 of FIG. 9 depicts input utility values associated with Recommended and Not Recommended consequences. As shown in this table, a Recommended consequence has an input utility value of 1 and a Not Recommended consequence has an input utility value of 0. By combining the input utility values and the Bayesian probabilities depicted in FIG. 12, the expected utility may be calculated according to Equation 13:

$\begin{matrix} {{Expectedutiilty} = {\sum\limits_{i = 1}^{n}{{consequenceresult} \times {inpututilityvalue}}}} & (13) \end{matrix}$

Where:

Expectedutility is the expected utility value; Consequence result is the Bayesian probability value associated with a consequence; Inpututilityvalue is the input utility value associated with a consequence; and n is the total number of consequences.

Accordingly, based on the input utility values depicted in FIG. 9 and the Bayesian probabilities depicted in FIG. 12, the expected utility value may be calculated using Equation 13. For example, for a user selection of a CaCO₃ drilling fluid type, the Bayesian probability associated with the Recommended consequence is 0.6923 (table 1100 in FIG. 11) and the input utility value associated with the Recommended consequence is 1 (table 900 in FIG. 9). Similarly, for a user selection of a CaCO₃ drilling fluid type, the Bayesian probability associated with the Recommended consequence is 0.3076 (table 1100 in FIG. 11) and the input utility value associated with the Recommended consequence is 0 (table 900 in FIG. 9). The calculation of the expected utility for a water swelling packer and a user selection of a CaCO₃ drilling fluid type is illustrated below in Equation 14:

$\begin{matrix} {{Expectedutiilty} = {{\sum\limits_{i = 1}^{n}{{consequenceresult} \times {inpututilityvalue}}} = {{{0.6923 \times 1} + {0.3076 \times 0}} = 0.6923}}} & (14) \end{matrix}$

The calculation the expected utility of the expected utility for an oil swelling packer and a user selection of a CaCO₃ drilling fluid type is illustrated below in Equation 15:

$\begin{matrix} {{Expectedutiilty} = {{\sum\limits_{i = 1}^{n}{{consequenceresult} \times {inpututilityvalue}}} = {{{0.8 \times 1} + {0.2 \times 0}} = 0.8}}} & (15) \end{matrix}$

The results of the calculations performed in Equations 14 and 15 are summarized in FIG. 13. FIG. 13 depicts a table 1300 showing the expected utility 1302 calculated above. As shown in this figure, the expected utility 1302 for a water swelling packer 1304 is 0.6293 (Equation 14), and the expected utility 1302 for an oil swelling packer 1306 is 0.8 (Equation 15). Thus, after inputting a drilling fluid type in the drilling fluid uncertainty node 406 in the BDN model 400, the BDN model 400 may output these expected utility values for the swelling packers associated with the swelling packer decision node 402. Based on these expected utility values, a user may select an optimal swelling packer for use with the selected drilling fluid type. For example, a user may select the swelling packer with the higher expected utility value, i.e., the oil swelling packer. That is, as shown in table 1300 of FIG. 13, the expected utility value of 0.8 associated with the oil swelling packer is greater than the expected utility value of 0.6923 associated with the water swelling packer.

In other interpretations, a user may input values for all of the uncertainty nodes of the BDN model 400 to determine the optimal selection of a swelling packer. In such instances, the consequences may be determined directly from the consequences node 408 of the BDN model 400, as depicted above in table 800 of FIG. 8. For example, a user may select inputs for the treating fluid uncertainty node 404 and the drilling fluid type uncertainty node 406 of the BDN model 400. Accordingly, FIG. 14 depicts a table 1400 showing the consequences for different swelling packers based on a user selection of a formate drilling fluid type and a lactic acid treating fluid. As shown in FIG. 14, the consequences may include a “Recommended” consequence 1402 and a “Not Recommended” consequence 1404 for both a water swelling packer 1406 and an oil swelling packer 1408. For a user selection of a formate drilling fluid type and a lactic acid treating fluid, table 800 of FIG. 8 shows a Recommended consequence value of 0 Not Recommended consequence value of 1 for a water swelling packer. Accordingly, the table 1400 shows that the water swelling packer 1406 has a Recommended consequence value of 0 and a Not Recommended consequence value of 1. Similarly, for a user selection of a formate drilling fluid type and a lactic acid treating fluid, table 800 of FIG. 8 shows a Recommended consequence value of 1 and a Not Recommended consequence value of 0 for an oil swelling packer. Thus, the table 1400 shows that the oil swelling packer 1408 has a Recommended consequence value of 1 and a Not Recommended consequence value of 0.

Based on the consequences described above, the expected utility for the different swelling packers may be determined using Equation 13 described above. For example, based on table 1400 of FIG. 14, the calculation of the expected utility for a water swelling packer is illustrated below in Equation 16:

$\begin{matrix} {{Expectedutiilty} = {{\sum\limits_{i = 1}^{n}{{consequenceresult} \times {inpututilityvalue}}} = {{{0 \times 1} + {1 \times 0}} = 0}}} & (16) \end{matrix}$

Similarly, the calculation of the expected utility for an oil swelling packer, using the values for consequences shown in table 1400 of FIG. 14, is illustrated below in Equation 17:

$\begin{matrix} {{Expectedutiilty} = {{\sum\limits_{i = 1}^{n}{{consequenceresult} \times {inpututilityvalue}}} = {{{1 \times 1} + {0 \times 0}} = 0}}} & (17) \end{matrix}$

FIG. 15 depicts a table 1500 illustrated the results of the calculations performed above in Equations 16 and 17. An expected utility 1502 for a water swelling packer 1504 and an oil swelling packer 1506 is illustrated in table 1500. Based on a user selection of a formate drilling fluid type and a lactic acid treating fluid, an expected utility value for the water swelling packer 1504 is 0 and the expected utility value for the oil swelling packer 1506 is 1. Based on these values, a user may select a swelling packer for use based on the BDN model 400. For example, a user may select the swelling packer with the higher expected utility value in table 1500, i.e., an oil swelling packer. Here again, a user may select an optimal swelling packer for use with the inputs, i.e., a selected treating fluid and drilling fluid type, provided to the BDN model 400. For example, a user may select the swelling packer with the higher expected utility value, i.e., the oil swelling packer. That is, as shown in table 1500 of FIG. 15, the expected utility value of 1 associated with the oil swelling packer is greater than the expected utility value of 0 associated with the water swelling packer.

With the above concepts in mind, the BDN modeling techniques described above may be applied to more complicated models for an a UBD system. Such models may serve as a training tool or a guide to aid engineers, scientists, or other users in selecting and executing operations of an UBD system. FIGS. 16-39 describe various BDN models related to UDB systems that may be implemented in a UBD expert system. As mentioned above, a UBD expert system may implement multiple models, such as one of or any combination of the BDN models described further below.

FIG. 16A depicts an example of a general UDB BDN model 1600 in accordance with an embodiment of the present invention. The general UBD BDN model 1600 may be divided into four sections: a formation section 1602, a planning phase section 1604, an equipment section 1606, and an operations types section 1608. The nodes of each section of the general UBD BDN model 1600 are described further below. As shown in FIG. 16, the connection lines 1609 indicate the dependencies between each node of the model 1600. The formation section 1602 of the general UBD BDN model 1600 includes a formation indicators uncertainty node 1610, a formation characteristics decision node 1612, and a formation consequences node 1614. The formation consequences node 1614 is dependent on the inputs to the formation indicators uncertainty node 1610 and the formation characteristics decision node 1612.

The planning phase section 1604 of the general UBD BDN model 1600 may include a planning phases uncertainty node 1616, a planning phases recommendations decision node 1618, and a planning phases consequences node 1620. As shown in the general UBD BDN model 1600, the planning phases consequences node 1620 is dependent on the inputs to the planning phases uncertainty node 1616 and the planning phases recommendations decision node 1618. The equipment section 1606 of the general UBD BDN model 1600 may include an equipment requirements uncertainty node 1622, an equipment recommendations decision node 1624, and an equipment consequences node 1626. As shown in FIG. 16A, the equipment consequences node 1626 is dependent on the inputs to the equipment requirements uncertainty node 1622 and the equipment recommendations decision node 1624.

Finally, the operation planning section 1608 of the general UBD BDN model 1600 includes an operations types uncertainty node 1628, an operations decision node 1630, and an operations consequences node 1632 that is dependent on the inputs to the nodes 1628 and 1630. The output from each section 1602, 1604, 1606, and 1608 of the general UBD BDN model 1600 is propagated to a final consequences node 1634 and a general UBD expert node 1636. Thus, the final consequences node 1634 is dependent on the consequences nodes 1614, 1620, 1626, and 1632 of each section of the general UBD BDN model 1600.

In some embodiments, the BDN model 1600 may be implemented in a user interface similar to the depiction of the model 1600 in FIG. 16A. In such embodiments, for example, each node of the model 1600 may include a button 1638 that enables a user to select a value for the node or see the determinations performed by a node. For example, as described below, a user may select (e.g., click) the button 1638A to select a formation indicator input for the model 1600, select the button 1638D to select a planning phases input for the model 1600, and so on. The inputs may be displayed in a dialog box or other user interface element.

FIGS. 16B-16I depict the selectable inputs for each node of the UBD BDN model 1600 in accordance with an embodiment of the present invention. FIGS. 16B and 16C depict the selectable inputs for the formation section 1602 of the BDN model 1600. FIG. 16B depicts inputs 1640 for the formation indicators node 1610. As shown in FIG. 16B, the inputs 1640 may include selectable formation indicators and may include N number of inputs from “formation_indicator_(—)1” to “formation_indicator_N.” As will be appreciated, in some embodiments the inputs 1640 may include associated probabilities, such as probabilities p_(—)1 through p_N. In some embodiments, a user may select one the inputs 1640 instead of using probabilities associated with the inputs 1640. The inputs 1640 may correspond to possible formation indicators corresponding to formations drilled by underbalanced drilling system. For example, in some embodiments the formation indicators may include the following: “Depeleted_reservoirs”, “Naturally_fractured_and_vugular_formation”, “Hard_rock_formation”, “Highly_permeable_formations,” and “Formations_susceptible_to_formation_damage_to_fluid_invasion”.

FIG. 16C depicts inputs for the formation characteristics decision node 1612 in accordance with an embodiment of the present invention. As shown in FIG. 16C, the inputs 1642 may include characteristics of different formations and may have N number of inputs from “characteristic_(—)1” to “characteristic N.” The inputs 1642 may correspond to characteristics of different formations when used with an underbalanced drilling system. For example, in some embodiments, the inputs 1642 may include the following: “Typically_exhibit_lost_circulation_and_differential_sticking_problems_and_a_consolidated_formation_is_an_excellent_UBD_candidate”, “Usually_exhibit_huge_losses_which_can_increase_the_chance_of_well_control_problems_or_lead_(—)to_differential_or_mechanical_sticking_making_this_type_of_formation_a_good_candidate_for_UBD”, “Usually_consolidated_and_therefore_can_sustain_UBD_and_UBD_will_provide_an_improve ment_in_ROP_and_bit_life_in_hard_rock”, “Typically_exhibit_lost_circulation_and_differential_sticking_problems_and_a_consolidated_formation_makes_an_excellent_UBD_candidate”,_and_“Fluid_invasion_can_be_minimized_or_even_eliminated_with_UBD.” As shown in the UBD BDN model 1600, the inputs for the formation indicators node 1610 and the considerations node 1612 are propagated to the consequences node 1614.

FIGS. 16D and 16E depict inputs for the planning phases section 1604 of the UBD BDN model 1600. FIG. 16D depicts the inputs for the planning phases uncertainty node 1616 in accordance with an embodiment of the present invention. The planning phases uncertainty node 1616 may provide for the input of planning phases for implementation of an UBD system. As shown in FIG. 16D, inputs 1644 may be planning phases and may include N number of inputs “phase_(—)1” through “phase_N.” As will be appreciated, in some embodiments the inputs 1644 to the uncertainty node 1616 may include associated probabilities, such as probabilities p_(—)1 to p_N associated with each input phase_(—)1 to phase N. In some embodiments, a user may select one the inputs 1644 instead of relying on the probability distribution associated with the inputs 1644. For example, in some embodiments the inputs 1644 may include “Phase_(—)1”, “Phase_(—)2”, “Phase_(—)3”, and Phase_(—)4”.

Additionally, FIG. 16E depicts inputs 1646 for the planning phases recommendations decision node 1618 in accordance with an embodiment of the present invention. The inputs 1646 may include planning phases recommendations and may have N number of inputs from “phase_recommendation_(—)1” through “phase_recommendation_N.” For example, in some embodiments, the inputs 1646 may include: “Planning_involves_preliminary_data_gathering_candidate_screening_and_feasibility_studies_to_result_in_a_quick_look_at_the_project_and_allow_for_budgetary_proposals_including_basic_equipment_and_personnel_set_up”, “Planning_involves_detailed_hydraulic_modeling_write_up_of_the_well_plan_to_be_added_to_the_client_drilling_plan_detailed_equipment_setup_and_drawings_and_operating_procedures_and_personnel_selection”, “Execution_may_or_may_not_involve_engineering_at_site_as_a_minimum_it_will_require_UBD_supervision_at_the_rig_location”, and “Close_out_will_involve_issuance_of_an_end_of_well_report_closure_of_any_service_qualify_issue_outstanding_and_archiving_data_gathered_during_the_well”.

FIGS. 16F and 16G depict inputs for the equipment section 1606 of the general UBD BDN model 1600. Accordingly, FIG. 16F depicts inputs 1648 for the equipment requirements uncertainty node 1622 in accordance with an embodiment of the present invention. As shown in FIG. 16F, the inputs 1648 may include equipment requirements and may have N number of inputs from “Equipment_(—)1” to “Equipment_N.” As will be appreciated, in some embodiments the inputs 1648 may include associated probabilities, such as respective probabilities p_(—)1 to p_N. associated with each input, and a user may select one the inputs 1648 instead of relying on the probability distribution associated with the inputs 1648. In some embodiments, for example, the inputs 1648 may include: “Drill_string_requirement_and_BHA_components”, “Rotating_control_device”, “Four-phase_separation_system”, “ESD_valve”, “Secondary_flow_line”, and “Geologic_sampler.” Additionally, FIG. 16G depicts inputs 1650 for the equipment recommendations decision node 1624 in accordance with an embodiment of the present invention. As shown in FIG. 16G, the inputs 1650 may be equipment recommendations and may include N number of inputs from “Equipment_Rec_(—)1” to “Equipment_Rec_N.” The inputs 1650 may include detailed recommendations for various equipment, such as the equipment input to the uncertainty node 1622, used in an UBD system.

Next, FIGS. 16H and 16I depict the inputs for the operations section 1608 of the general UBD BDN model 1600. FIG. 16H depicts inputs 1652 for the operations types uncertainty node 1628 in accordance with an embodiment of the present invention. The inputs may include operation types for operating a UBD system and may include N number of inputs from “operation_type_(—)1” to “operation_type_N.” In some embodiments, the inputs 1652 may include “Low_pressure_well”, and “High_pressure_well.” Similarly, FIG. 16I depicts inputs 1654 for the operations types recommendations decision node 1630 in accordance with an embodiment of the present invention. The inputs 1654 to the decision node 1630 may include operations type recommendations and may have N number of inputs from “Operation_rec_(—)1” to “Operation_rec_N.” The inputs 1654 may be detailed recommendations for operation types for operating a UBD system.

After selecting one or more inputs for the nodes of the different sections 1602, 1604, 1606, and 1610 of the UBD BDN model 1600, the inputs may be propagated to the various consequence nodes 1614, 1620, 1626, and 1632 of each section, and then to the final consequences node 1634. The UBD BDN model 1600 may propagate the inputs using the Bayesian probability determinations described above in Equations 1, 2, and 4. By using the probabilities associated with the inputs, the UBD BDN model 1600 may then provide recommendations or expected utilities at each consequence node 1614, 1620, 1626, and 1632 for each section. Additionally, the UBD BDN model 1600 may provide recommendations or expected utilities at the final consequence node 1632 based on the propagated outputs from the consequence nodes 1614, 1620, 1626, and 1632. In some embodiments, the uncertainty nodes of the UBD BDN model 1600 may have inputs with associated probabilities. A user may select an input for one or more uncertainty nodes and view the recommendations based on the propagation of the selected input. For example, a user may select an input for the formation indicators node 1610 and receive a recommended formation consideration at the consequences node 1614. For example, a user may also select an input for the planning phases uncertainty node 1616 and receive a recommended planning phase recommendation (based on the inputs to the planning phases recommendations decision node 1618) from the consequences node 1620. One or more of the sections 1602, 1604, 1606, and 1608 of the UBD BDN model 1600 may be used; thus, a user may use one or more sections of the UBD BDN model 1600 but not use the remaining sections of the UDB BDN model 1600.

FIGS. 17 and 18 depict selection of inputs and a corresponding output of the formation section 1602 of the UBD BDN model 1600 in accordance with an embodiment of the present invention. As shown in FIG. 17, a user may select an input for the formation indicator uncertainty node 1610, such as indicator based on a formation to be drilled via a UBD system. As shown in FIG. 17, for example, a user may select “Naturally_fractured_and_singular_formation” as an input 1700 for the formation indicator uncertainty node 1610. In some embodiments, the input 1700 may be displayed, such as in a dialog box or other user interface element, to indicate the input to the uncertainty node 1610. After entering an input for the formation indicators uncertainty node 1610, the user may select the consequences node 1614 to view the recommendations based on the selected input and the inputs to the decision node 1612.

FIG. 18 depicts an example of the output from the consequences node 1614 of the formation section 1602 based on the input described above in FIG. 17 and in accordance with an embodiment of the present invention. As shown in FIG. 18, in some embodiments the output may be provided as a table 1800 displaying probability states 1802 for formation characteristics 1804 (as input to the formation characteristics decision node 1612). As shown in table 1800, for example, the formation consideration “Formation_consideration_(—)2” has a probability state of 0.1. The other considerations shown in table 1800 have probability states of 0. Thus, a user may decide to base a UBD system implementation on the consideration having the highest expected probability state in the table 1800. In other embodiments, the output may be provided as a dialog box displaying the recommendation having the highest expected probability state (such that other recommendations having lower probability states are not displayed).

As mentioned above, in some embodiments a UBD expert system may also include a flow UBD BDN model. FIGS. 19A-19H depicts a flow UBD BDN model 1900 in accordance with an embodiment of the present invention. The flow UBD BDN model 1900 may include three sections: a tripping section 1902, a connection section 1904, and a flow drilling section 1906. The nodes of each section are described further below. As shown in FIG. 19, the connection lines 1907 indicate the dependencies between each node of the flow UDB BDN model 1900. The tripping section 1902 of the flow UBD BDN model 1900 includes a tripping types uncertainty node 1908, a permeability level uncertainty node 1910, a tripping options decision node 1912, and a tripping recommendation consequences node 1914. The tripping recommendation consequences node 1914 is dependent on the inputs to the uncertainty nodes 1908 and 1910 and the decision node 1912. The inputs to these nodes will be discussed further below.

The connection section 1904 of the flow UBD BDN model 1900 includes a connection types uncertainty node 1916, a connection options decision node 1918, and a connection recommendations consequence node 1920. The connection recommendations consequence node 1920 is dependent on inputs to the uncertainty node 1916 and the decision node 1918. Finally, the flow drilling section 1906 includes a flow drilling types uncertainty node 1922, a flow drilling options decision node 1924, and a flow drilling recommendations consequence node 1926. As shown in FIG. 19, the flow drilling recommendations consequence node 1926 is dependent on the uncertainty node 1922 and the decision node 1924. The output from each consequence node 1914, 1920, and 1926 of each section 1902, 1904, and 1906 may be propagated to a final consequences node 1928 and a flow UBD expert node 1930. Thus, the final consequences node 1928 is dependent on the consequences nodes 1914, 1920, and 1926.

In some embodiments, the flow BDN model 1900 may be implemented in a user interface similar to the depiction of the model 1600 in FIG. 16A. In such embodiments, for example, each node of the model 1900 may include a button 1932 that enables a user to select a value for the node or see the determinations performed by a node. For example, as described below, a user may select (e.g., click) the button 1932A to select a tripping input for the model 1600, select the button 1932E to select a connection input for the model 1600, and so on.

FIGS. 19B-19H depict the inputs for each node of the flow UBD BDN model 1600 in accordance with an embodiment of the present invention. In these figures, the various section delineations and associated reference numbers may be omitted for clarity. FIGS. 19B-19D depict the inputs for the nodes of the tripping section 1902. For example, FIG. 19B depicts inputs 1934 for the tripping types uncertainty node 1908 in accordance with an embodiment of the present invention. As shown in FIG. 19B, the inputs 1934 may types of tripping operations for a UBD system and may have N inputs from “tripping_(—)1” through “tripping_N.” In some embodiments, for example, the inputs 1934 may include “run_into_the_hole_(RIH)” and “pull_out_of_hole_(POH)”. As will be appreciated, in some embodiments the inputs 1934 may include associated probabilities, such as respective probabilities p_(—)1 to p_N associated with each input. Alternatively a user may select one the inputs 1934 to view recommendations for a specific input.

FIG. 19C depicts inputs 1936 for the permeability level uncertainty node 1910 of the flow UBD BDN model 1900 in accordance with an embodiment of the present invention. The inputs 1936 may include permeability levels and may have N number of inputs from “perm_level_(—)1” to “perm_level_N.” For example, in some embodiments the selectable permeability levels 1936 may include “Low” and “High”. As will be appreciated, in some embodiments the inputs 1936 may include associated probabilities, such as respective probabilities p_(—)1 to p_N. associated with each input, and a user may select one the inputs 1936 instead of using the probability distribution associated with the inputs 1936.

Next, FIG. 19D depicts inputs 1938 for the tripping options decision node 1912 in accordance with an embodiment of the present invention. As shown in FIG. 19D, the inputs 1938 may include tripping options 1938 and may have N number of inputs from “tripping_option_(—)1” to “tripping_option_N.” In some embodiments, for example, the inputs 1938 may include “RCD engaged surface pressure needs to be constant by releasing fluid through choke”, “Turn_off_pump_and_close_choke_and_do_not_fill_hole”, “Use_mud_cap”, and “Turn_off_pump_and_close_choke_and_fill_holes_displacement_volume.”

FIGS. 19E and 19F depict inputs for the connection section 1904 of the flow UBD BDN model 1600. FIG. 19E depicts inputs 1940 for the connection types uncertainty node 1916 in accordance with an embodiment of the present invention. As shown in FIG. 19E, the inputs 1940 may include connection types and may have N number of inputs from “connection_(—)1” to “connection_N.” For example, in some embodiments, the selectable connections 1940 may include “On_connection” and “After_connection”. As will be appreciated, in some embodiments the inputs 1940 may include associated probabilities, such as respective probabilities p_(—)1 to p_N associated with each input, and a user may select one the inputs 1940 instead of using the probability distribution associated with the inputs 1940. Additionally, FIG. 19F depicts inputs 1942 for the connection options decision node 1918. The inputs 1940 may include options for connections in a UBD system and may have N number of inputs from “connection_option_(—)1” to “connection_option_N.” In some embodiments, the inputs 1940 may include “Shutin_RCD_and_choke_system_and_keep_pump_on” and “Start_pump_and_open_choke_slowly_and_lower_pipe.” The inputs described above may be propagated to the connection recommendation consequences node 1920.

Finally FIGS. 19G and 19H depict inputs for the flow drilling section 1906 of the flow UBD BDN model 1900. FIG. 19G depicts inputs 1944 for the flow drilling types uncertainty node 1922 in accordance with an embodiment of the present invention. The inputs 1944 include flow drilling types and may have N number of inputs from “Flow_drilling_(—)1” to “Flow_drilling_N.” The inputs 1944 may include different types of flow drilling used in a UBD system. In some embodiments, the inputs 1944 may include “Flow_drilling_with_normal_returns”, “Flow_drilling_with_formation_gas_or_fluid_returns”, “Flow_drilling_with_no_returns”, “Flow_drilling_with_no_returns_and_with_gas_rising_to_the_surface”, “Drilling_in_a_long_horizontal_or_high_angle_well”, “Circulating_density_changes”, and “Gel_strength_and_inertial_forces.” As will be appreciated, in some embodiments the inputs 1944 may include associated probabilities, such as respective probabilities p_(—)1 to p_N. associated with each input. Alternatively a user may select one the inputs 1944 to view recommendations for a specific input. Additionally, FIG. 19H depicts inputs 1946 for the flow drilling options decision node 1924 in accordance with an embodiment of the present invention. The inputs 1946 for the decision node 1924 may be flow drilling options and may have N number of inputs from “flow_drilling_option_(—)1” to “flow drilling_option_N.” The inputs 1946 options may include options for various types of flow drilling.

After selecting one or more inputs for the nodes of the different sections 1902, 1904, and 1906 of the flow UBD BDN model 1900, the inputs may be propagated to the various consequence nodes 1914, 1920, and 1926 of each section, and then to the final consequences node 1928. The flow UBD BDN model 1900 may propagate the inputs using the Bayesian probability determinations described above in Equations 1, 2, and 4. By using the probably states associate with the inputs, the flow UBD BDN model 1900 may then provide recommendations or expected utilities at each consequence node 1914, 1920, and 1926. Additionally, the flow UBD BDN model 1900 may provide recommendations or expected utilities at the final consequence node 1928 based on the propagated outputs from the consequence nodes 1914, 1920, and 1926. In some embodiments, the uncertainty nodes of the UBD BDN model 1900 may have inputs with associated probability distributions. In some embodiments, a user may select an input for one or more uncertainty nodes and view the recommendations based on the propagation of the selected input. For example, a user may select an input for the tripping types uncertainty node 1908, the permeability level uncertainty node 1910, or both, and receive a recommendation (based on the inputs to the tripping options decision node 1912) at the consequences node 1914. Similarly, a user may select an input for the connection types uncertainty node 1916 and receive a planning phase recommendation (based on the inputs to the connection options decision node 1918) from the consequences node 1920. One or more sections 1902, 1904, and 1906 of the flow UBD BDN model 1900 may be used; consequently, a user may use one or more sections of the flow UBD BDN model 1900 and not use the remaining sections of the UDB BDN model 1900.

FIGS. 20A-20B and 21 depict selections of inputs and a corresponding output for the tripping section 1902 of the flow UBD BDN model 1900. For example, as shown in FIG. 20A, a user may select an input for the tripping types uncertainty node 1908 based on a tripping operation used or to be implemented and in accordance with an embodiment of the present invention. As shown in FIG. 20A, for example, a user may select “run_in_hole_RIH” as an input 2000 for the node 1908. The selected input 2000 may be displayed, such as in a dialog box or other user interface element, to indicate the input to the uncertainty node 1908. Additionally, a user may select inputs for other nodes, such as the permeability uncertainty node 1910. FIG. 20B depicts selection of an input 2002 for the permeability uncertainty node 1910 in accordance with an embodiment of the present invention. For example, as shown in FIG. 20B, a user may select “High” as the input 2002 for the permeability uncertainty node 1910. The selected input 2002 may be displayed, such as in a dialog box or other user interface element, to indicate the input for the node 1910.

After entering inputs for the tripping section 1902 of the flow UBD BDN model 1900, a user may select the tripping recommendation consequences node 1914 to view the recommendations determined by the flow UBD BDN model 1900. As shown in FIG. 21, in some embodiments the output from the tripping recommendation consequences node 1914 may be provided as a table 2100 displaying expected utilities 2102 (e.g., “Recommended” and “Not Recommended”) for tripping options 2104, i.e., the inputs to the tripping options decision node 1912. Each of the tripping options may include an expected utility value, such as 1 or 0, calculated according to Equation 13 discussed above. For example, table 2100 depicts a the tripping option “Use_mud_cap” as having a Recommended expected utility value of 1 and a Not Recommended expected utility value of 0. The other tripping options depicted in FIG. 21 may have a Recommended expected utility value of 0 and a Not Recommended expected utility value of 1. Thus, a user may decide to implement the tripping option having the highest expected utility depicted in table 2100, such as the “Use_mud_cap” tripping option in the present example. In other embodiments, the output may be provided as a table displaying probability states for recommendations or a dialog box displaying the recommendation having the highest expected probability state (such that other recommendations having lower probability states are not displayed).

In some embodiments, a UBD expert system may also include a gaseated UBD BDN model. FIGS. 22A-22I depict a gaseated UBD BDN model 2200 in accordance with an embodiment of the present invention. As shown in FIG. 22A, the gaseated UBD BDN model 2200 may include four sections: a gas injection section 2202, a gas and fluid volume section 2204, a kick section 2206, and an operational section 2208. The nodes of each of these sections are described further below. As also shown in FIG. 22, connection lines 2209 indicate the dependencies between each node of the gaseated UBD BDN model 2200. The gas injection process section 2202 includes a gas injection uncertainty node 2210, a gas injection process characteristics decision node 2212, and a consequences node 2214. As shown in the model 2200, the consequences node 2214 is dependent on the uncertainty node 2210 and the decision node 2212.

Next, the gas and fluid volume section 2204 includes a gas and fluid volume limits uncertainty node 2216, a requirements for gas and fluid volume limits decision node 2218, and a consequences node 2220 that is dependent on the uncertainty node 2216 and the decision node 2218. Additionally, the kicks section 1606 includes a kick type uncertainty node 2222, a well kicks recommendation decision node 2224, and a consequences node 2226 dependent on the uncertainty node 2222 and the well kicks recommendation node 2224. Finally, the operational section 1618 includes an operational considerations uncertainty node 2228, an operational recommendations decision node 2230, and a consequences node 2232. The consequences node 2232 is dependent on the uncertainty node 2228 and the operational recommendations node 2230. The output from each consequence node 2214, 2220, 2226, and 2232 of each section 2202, 2204, 2206, and 2208 may be propagated to a final consequences node 2234 and a flow UBD expert node 2234. Thus, the final consequences node 2234 is dependent on the consequences nodes 2214, 2220, 2226, and 2232.

As described above with regard to the other BDN models, in some embodiments the flow BDN model 2200 may be implemented in a user interface similar to the depiction of the model 2200 in FIG. 22. In such embodiments, for example, each node of the model 2200 may include a button 2236 that enables a user to select a value for the node or see the determinations performed by a node. For example, as described below, a user may select (e.g., click) the button 2236A to select a gas injection process input for the model 1600, select the button 2236D to select a gas and fluid volume limit input for the model 2200, and so on.

FIGS. 22B-22I depict the inputs for each node of the gaseated UBD BDN model 2200 in accordance with an embodiment of the present invention. In some figures, the section delineations and some reference numbers may be omitted for clarity. For example, FIGS. 22B and 22C depict the inputs for the gas injection section 2202 of the gaseated UBD BDN model 2200. Accordingly, FIG. 22B depicts inputs 2238 for the gas injection process uncertainty node 2210 in accordance with an embodiment of the present invention. The inputs 2238 may include gas injection processes and may include N number of inputs from “gas_injection_(—)1” to “gas_injection_N.” As will be appreciated, in some embodiments the inputs 2238 may include associated probabilities, such as probabilities p_(—)1 through p_N. The inputs 2238 may include different gas injection processes used in a UBD system. For example, in some embodiments the inputs 2238 may include “Drill_pipe_injection”, “Drill_pipe_jet_sub”, “Parasite_tubing_tubing_string”, and “Concentric_casing_string_or_dual_casing_string.” Additionally, FIG. 22C depicts inputs 2240 for the gas injection process characteristics decision node 2212 in accordance with an embodiment of the present invention. The inputs may include characteristics of different gas injection processes for gaseated UBD systems and may include N number of inputs from “Characteristic_(—)1” to “Characteristic_N.” In some embodiments, the characteristics may include benefits and challenges of using a particular gas injection process.

FIGS. 22D and 22E depict the inputs for nodes of the gas and fluid volume section 2204. For example, FIG. 22D depicts inputs 2242 for the gas and fluid volume limits node 2216 in accordance with an embodiment of the present invention. The inputs 2242 may be gas and fluid volume limits and may include N number of inputs from “volume_limit_(—)1” to “volume_limit_(—)2.” As will be appreciated, in some embodiments the inputs 2242 may include associated probabilities, such as probabilities p_(—)1 through p_N. The inputs 2242 may include types and definitions of limits on gas and fluid volumes for a gaseated UBD system. For example, in some embodiments the inputs 2242 may include “Gas_limit”, “Liquid_limit”, “Back_pressure”, and “Motor_constraints.” Additionally, FIG. 22E depicts inputs 2244 for the requirements for gas and fluid volume limits decision node 2218 in accordance with an embodiment of the present invention. As shown in FIG. 22E, the inputs 2244 may be gas and fluid volume limit requirements and may include N number of inputs from “Volume_limit_req_(—)1” to “Volume_limit_req_(—)2.” The inputs 2244 may correspond to requirements for implementing specific gas and fluid volume limits for UBD systems.

FIGS. 22F and 22G depict inputs for nodes of the kick section 1606 of the gaseated UBD BDN model 2200. Accordingly, FIG. 22F depicts inputs 2246 for the kick type uncertainty node 2222 in accordance with an embodiment of the present invention. The inputs to the uncertainty node 2222 may include types of well kicks, and the inputs 2246 may include N number of inputs from “kick_type_(—)1” to “kick_type_N. As will be appreciated, in some embodiments the inputs 2246 may include associated probabilities, such as probabilities p_(—)1 through p_N. The inputs 2246 may correspond to types of kicks that may be experienced in a gaseated UBD BDN system. For example, in some embodiments the inputs 2246 may include “Gas_flow” ‘and “Water_oil_flow.” Additionally, FIG. 22G depicts inputs 2248 for the well kicks recommendation decision node 2224 in accordance with an embodiment of the present invention. The inputs 2248 may include recommendations for responding to well kicks that may be encountered in a UBD system. As shown in FIG. 22G, the inputs 2248 may include N number of inputs from “well kick_rec_(—)1” to “well_kick_rec_N.”

Finally, FIGS. 22H and 221 depict inputs for the nodes of the operational section 1608 of the gaseated UBD BDN model 2200. FIG. 22H depicts inputs 2250 for the operational considerations uncertainty node 2228 in accordance with an embodiment of the present invention. As shown in this figure, the inputs may be operational considerations 2250 and may include N number of inputs from “Operational_considerations_(—)1” to “Operational_considerations_N.” As will be appreciated, in some embodiments the inputs 2250 may include associated probabilities, such as probabilities p_(—)1 through p_N. The inputs 2250 may include various considerations related to operation of a gaseated UBD system. For example, in some embodiments the inputs 2250 may include: “Cost”, “Pressure_surges”, “Unloading_the_casing”, “Connections”, “Stripping_in_unbalanced_operation”, “Snubbing”, “Inhibition”, and “Periodic_kill”. In some embodiments, the considerations may include concerns, challenges, and other considerations in operating a gaseated UBD system.

FIG. 22I depicts inputs 2252 for the operational recommendations decision node 2230 in accordance with an embodiment of the present invention. The inputs 2252 to the node 2230 may be operational recommendations 2252 and may include N number of inputs from “Operation_rec_(—)1” and “Operational_rec_N”. The inputs 2252 may include recommendations for operating a gaseated UBD system in view of the considerations entered into the model 2200.

Here again, after selecting one or more inputs for the nodes of the different sections 2202, 2204, 2206, and 2208 of the gaseated UBD BDN model 1900, the inputs may be propagated to the various consequence nodes 2214, 2220, 2226, and 2232 of each section, and then to the final consequences node 2234, using the Bayesian probability determinations described above in Equations 1, 2, and 4. By using the probably states associate with the inputs, the gaseated UBD BDN model 2200 may then provide recommendations or expected utilities at each consequence node 2214, 2220, 2226, and 2232. Additionally, the gaseated UBD BDN model 2200 may provide recommendations or expected utilities at the final consequence node 2234 based on the propagated outputs from the consequence nodes 2214, 2220, 2226, and 2232. In some embodiments, the uncertainty nodes of the UBD BDN model 2200 may have inputs with associated probability distributions. In some embodiments, a user may select an input for one or more uncertainty nodes and view the recommendations based on the propagation of the selected input. For example, a user may select an input for the gas injection process uncertainty node 2210 and receive a recommendation (based on the inputs to the gas injection processes characteristics decision node 2212) at the consequences node 2214. Similarly, a user may select an input for the kick type uncertainty node 2222 and receive a recommendation (based on the inputs to the well kicks recommendations decision node 2224) from the consequences node 2226. One or more sections 2202, 2204, 2206, and 2208 of the gaseated UBD BDN model 2200 may be used; consequently, a user may use one or more sections of the gaseated UBD BDN model 2200 and not use the remaining sections of the gaseated UDB BDN model 2200.

FIGS. 23A and 23B depict selections of inputs and a corresponding output for the gas injection section 2202 of the gaseated UBD BDN model 2200. As shown in FIG. 23A, a user may select an input 2300 for the gas injection process uncertainty node 2210, such as a gas injection process used in a UBD system, in accordance with an embodiment of the present invention. As shown in FIG. 23A, for example, a user may select “Concentric_casing_string_or_dual_casing_string” as the input 2300 for the node 2210. The selected input 2300 may be displayed, such as in a dialog box or other user interface element, to indicate the input to the node 2210.

After entering inputs for the gas injection section 2202 of the gaseated UBD BDN model 2200, a user may select the consequences node 2214 to view the recommendations determined by the gaseated UBD BDN model 2200. FIG. 23B depicts an example of an output 2302 from the consequences node 2214 based on the input described above in FIG. 23A and in accordance with an embodiment of the present invention. As shown in FIG. 23B, in some embodiments the output 2302 may be presented as a dialog box or other user interface element displaying the recommended output from the consequences node 2214. For example, the output 2302 may be based on a determination of a recommendation with the highest Bayesian probability state as determined from the inputs received from the uncertainty node 2310 and the decision node 2312. As shown in FIG. 23B, in some embodiments output 2302 may provide text describing the characteristics (e.g., “Characteristic text), such as benefits and challenges, for the gas injection process input into the gas injection process uncertainty node 2210. Thus, a user may view various recommendations for various inputs to aid in implementation of a gaseated UBD system. In other embodiments, as described above, the output from a BDN model may be provided as a table of expected utility values, a table of Bayesian probability states for each recommendation, or other suitable outputs.

Additionally, in some embodiments, a UBD expert system may also include a foam UBD BDN model for use in determining optimal operations for a foam UBD system. FIGS. 24A-24E depict a foam UBD BDN model 2400 in accordance with an embodiment of the present invention. The UDB BDN model 2400 may include two sections: a foam systems considerations section 2402 and a foam system design section 2404. Each of these sections is described further below. Additionally, the connections lines 2405 depicted in FIG. 24A illustrate the dependencies between the nodes of the foam UBD BDN model 2400.

The foam systems considerations section 2402 includes a foam systems considerations uncertainty node 2406, a foam systems considerations decision node 2408, and a consequences node 2410 that is dependent on the uncertainty node 2406 and the decision node 2408. The foam system design section 2404 includes a foam system designs uncertainty node 2412, a foam systems designs recommendations decision node 2414, and a consequences node 2416 that is dependent on the uncertainty node 2412 and the decision node 2414. The output from each consequence node 2410 and 2416 may be propagated to a final consequences node 2418 and a UBD expert node 2420.

As described above with regard to the other BDN models, in some embodiments, the foam UBD BDN model 2400 may be implemented in a user interface similar to the depiction of the model 2400 in FIG. 24A. In such embodiments, for example, each node of the foam UBD BDN model 2400 may include a button 2422 that enables a user to select an input for the node or see the determinations performed at a node. For example, as described below, a user may select (e.g., click) the button 2244A to select a consideration input for the model 2400, select the button 2244D to select a foam systems design input for the model 2400, and so on.

FIGS. 24B-24E depict the inputs for nodes of the foam UBD BDN model 2400 in accordance with an embodiment of the present invention. In some of these figures, the section delineations and some reference numbers may be omitted for clarity. FIGS. 24B and 24C depict the inputs for the foam systems considerations section 2402 of the foam UBD BDN model 2400. FIG. 24B depicts inputs 2424 for the foam systems considerations node 2406 in accordance with an embodiment of the present invention. The inputs 2424 may include N number of inputs from “Foam_consideration_(—)1” to “Foam_consideration_N.” As will be appreciated, in some embodiments the inputs 2424 may include associated probabilities, such as probabilities p_(—)1 through p_N. The inputs 2424 may include considerations, such as challenges, technical limits, and so on, for implementing a foam UBD system. For example, in some embodiments the inputs 2424 may include “Cost”, “Hot_holes”, “Foam_breakdown”, and “One_pass_system_or_disposable_foam”.

FIG. 24C depicts inputs 2426 for the foam systems considerations recommendations decision node 2408 in accordance with an embodiment of the present invention. The inputs for the decision node 2408 may be foam systems recommendations and may include N number of inputs from “Foam_system_consideration_rec_(—)1” to “Foam_system_consideration_rec_N”. The inputs 2426 may include recommendations for implementing foam UBD systems.

Next, FIGS. 24D and 24E depict the inputs for the foam systems design section 2402 in accordance with an embodiment of the present invention. FIG. 24D depicts the inputs 2428 for the foam systems designs uncertainty node 2412 in accordance with an embodiment of the present invention. The inputs 2428 may include N number of inputs from “foam_systems_design_(—)1” to “foam_systems_design_N.” As will be appreciated, in some embodiments the inputs 2428 may include associated probabilities, such as probabilities p_(—)1 through p_N. The inputs 2428 may include design considerations for designing a foam UBD system. For example, the selectable foam systems designs 2428 may include: “General_operational_ideas”, “Bottom_hole_pressure_reduction”, “The_effect_of_fluid_and_gas_volumes_on_hole_cleaning_and_motor_operations”, “Making_a_connection”, and “Making_trips”. FIG. 22E depicts inputs 2430 for the foam systems designs recommendations decision node 2414 in accordance with an embodiment of the present invention. The inputs 2430 to the node 2414 may be foam systems designs recommendations and may include N number of inputs from “foam_systems_designs_details_(—)1” to “foam_systems_designs_details_N”. The selectable inputs 2430 may include detailed recommendations for of various foam system designs input into the foam UBD BDN model 2400.

As described above, after selecting one or more inputs for the nodes of the different sections 2402 and 2402 of the flow UBD BDN model 2400, the inputs may be propagated to the consequence nodes 2410 and 2416 of each section, and then to the final consequences node 2418, using the Bayesian probability determinations described above in Equations 1, 2, and 4. By using the probably states associate with the inputs, the flow UBD BDN model 2400 may then provide recommendations or expected utilities at each consequence node 2410 and 2416\. Additionally, the flow UBD BDN model 2400 may provide recommendations or expected utilities at the final consequence node 2418 based on the propagated outputs from the consequence nodes 2410 and 2416. In some embodiments, the uncertainty nodes of the flow UBD BDN model 2400 may have inputs with associated probability distributions. In some embodiments, a user may select an input for one or more uncertainty nodes and view the recommendations based on the propagation of the selected input. For example, a user may select an input for the foam systems considerations uncertainty node 2406 and receive a recommendation (based on the inputs to the foam systems considerations decision node 2408) at the consequences node 2410. Similarly, a user may select an input for the foam systems design uncertainty node 2412 and receive a recommendation (based on the inputs to the foam systems decision node 2414) from the consequences node 2416. One or both sections 2402 and 2404 of the flow UBD BDN model 2400 may be used; consequently, a user may use one or both sections of the flow UBD BDN model 2400 and not use the remaining sections of the flow UDB BDN model 2400.

FIGS. 25A and 25B depict selections of inputs and corresponding outputs for the foam UBD BDN model 2400 in accordance with an embodiment of the present invention. As depicted in FIG. 25A, a user may select an input 2500 for the foam systems considerations uncertainty node 2406, such as specific considerations expected in a current or prospective foam UBD system. As shown in FIG. 25A, a user may select “hot_holes” as the input 2500 for the uncertainty node 2406. The selected input 2500 may be displayed, such as in a dialog box or other user interface element, to indicate the input to the node 2406.

FIG. 25B depicts an example of an output 2502 from the consequences node 2408 based on the input described above in FIG. 25A and in accordance with an embodiment of the present invention. As shown in FIG. 25B, in some embodiments the output 2502 may be presented as a dialog box displaying the recommendation from the consequences node 2410. For example, the output 2502 may be based on a determination of a recommendation with the highest Bayesian probability state as determined from inputs received from the uncertainty node 2406 and the decision node 2408. As shown in FIG. 25B, in some embodiments the output may include text describing the recommendation (e.g., “Recommendations text”) for the selected consideration input into the model 2400. Accordingly, a user may view various recommendations for various inputs to aid in implementation of a flow UBD system. In other embodiments, as described above, the output from a BDN model may be provided as a table of expected utility values, a table of Bayesian probability states for each recommendation, or other suitable outputs. As will be appreciated, the other sections of the flow UBD BDN model 2400 may receive inputs and provide outputs in a similar manner as described above and illustrated FIGS. 25A and 25B.

As mentioned above, the UBD expert system may also include an air and gas UBD BDN model for providing optimal operations for an air and gas UBD system. FIGS. 26A-26I depict an air and gas UBD BDN model 2600 and associated inputs in accordance with an embodiment of the present invention. The air and gas UBD BDN model 2600 may include four sections, the nodes of which are described further below: a rotary and hammer drilling section 2602, a considerations section 2604, a gas drilling operations section 2606, and a rig equipment section 2608. The air and gas UBD BDN model 2600 depicted in FIG. 26A also includes connection lines 2609 that indicate dependencies between the nodes of the air and gas UBD BDN model 2600.

The rotary and hammer drilling section 2602 of the air and gas UBD BDN model 2600 may include a rotary and hammer drilling uncertainty node 2610, a rotary and hammer drilling recommendations decision node 2612, and a consequences node 2614 that is dependent on the uncertainty node 2610 and the decision node 2612. The considerations section 2604 may include a gas drilling considerations uncertainty node 2616, a gas drilling considerations decision node 2618, and a consequences node 2620 that is dependent on the uncertainty node 2616 and the decision node 2618. Additionally, the gas drilling operations section 2606 includes a gas drilling operations uncertainty node 2622, a gas drilling recommendations decision node 2624, and a consequences note 2626 that is dependent on the uncertainty node 2622 and the decision node 2624. Finally, as also shown in FIG. 26A, the rig equipment section 2610 includes a gas drilling rig equipment uncertainty node 2628, a gas drilling rig equipment recommendations decision node 2630, and a consequences node 2632 that is dependent on the uncertainty node 2628 and the decision node 2630. The output from each of the consequences nodes 2614, 2620, 2626, and 2632 of each section may be propagated to a final consequences node 2634 and an air and gas UBD expert system node 2636. Accordingly, the final consequences node 2634 is dependent on the consequences nodes 2614, 2620, 2626, and 2632, as illustrated by the connection lines 2609.

In some embodiments, as described with regard to the other BDN models, the air and gas BDN model 2600 may be implemented in a user interface similar to the depiction of the model 2200 in FIG. 22. In such embodiments, for example, each node of the model 2600 may include a button 2638 that enables a user to select a value for the node or see the determinations performed by a node. For example, as described below, a user may select (e.g., click) the button 2638A to select a rotary and hammer drilling input for the model 2600. Similarly, a user may select (e.g., click) the button 2638D to select a considerations input for the model 2600. As noted above, evidence (inputs) may be introduced at any nodes of the model 2600 and propagated throughout the air and gas BDN model 2600 using the Bayesian logic described above.

FIGS. 26B-26I depict the inputs for each node of the air and gas UBD BDN model 2600 in accordance with an embodiment of the present invention. In some figures, the section delineations and some reference numbers may be omitted for clarity. FIGS. 26B and 26C depict the inputs for the rotary and hammer drilling section 2602 of the air and gas UBD BDN model 2600. Accordingly, FIG. 26B depicts inputs 2640 for the rotary and hammer drilling uncertainty node 2610 in accordance with an embodiment of the present invention. The inputs 2640 to the uncertainty node 2610 may include rotary and hammer drilling types and may include N number of inputs from “rotary_and_hammer_(—)1” to “rotary_and_hammer_N.” As will be appreciated, in some embodiments the inputs 2640 may include associated probabilities, such as probabilities p_(—)1 through p_N. The inputs 2640 may include different types of rotary drilling, hammer drilling, or both that may be used in an air and gas UBD system. For example, in some embodiments, the inputs 2640 may include: “Rotary_drilling”, “Hammer_drilling”, “Horizontal_drilling_with_air_hammers”, and “Dual_drill_pipe”. Similarly, FIG. 26C depicts inputs 2642 for the rotary and hammer drilling recommendations decision node 2612 in accordance with an embodiment of the present invention. The inputs to the decision node 2612 may be rotary and hammer drilling recommendations and may include N number of inputs from “rotary_and_hammer_rec_(—)1” to “rotary_and_hammer_rec_N.” The inputs 2642 may include recommended practices for different rotary and hammer drilling types input into the model 2600.

Next, FIGS. 26D and 26E depict inputs for the gas drilling considerations section 2604 of the air and gas UBD BDN model 2600 in accordance with an embodiment of the present invention. FIG. 26D depicts inputs 2644 for the gas drilling considerations uncertainty node 2616 in accordance with an embodiment of the present invention. As shown in FIG. 26D, the inputs 2644 may include N number of inputs ranging from “Gas_drilling_considerations_(—)1” to “Gas_drilling_considerations_N.” As will be appreciated, in some embodiments the inputs 2644 may include associated probabilities, such as probabilities p_(—)1 through p_N. The inputs 2644 may include different considerations or combinations thereof related to gas drilling implementations in a UBD drilling system. In some embodiments, the considerations may include limits, extremes, challenges, and the like associated with gas drilling. As such, in some embodiments, the inputs 2644 may include, for example: “Water_or_wet_holes”, “Hole_enlargment”, “Depth_limits”, “Floating_bed”, “Fishing_operations”, “Flashback_fire_in_the_blooie_line_from_the_flare”, “Downhole_fire”, and “Air_drilling_and_hydrogen_sulfide_gas”. FIG. 26E depicts inputs 2646 for the gas drilling considerations recommendations decision node 2618 in accordance with an embodiment of the present invention. The inputs 2646 may include N number of recommendations ranging from “gas_drilling_considerations_rec_(—)1” to “gas_drilling_considerations_rec_N”. The inputs 2646 may include recommendations, such as recommended practices, for gas drilling in an UBD system or other recommendations for the considerations input in to the model 2600.

Next, FIGS. 26F and 26G depict inputs for the gas drilling operations section 2606. Accordingly, FIG. 26F depicts inputs 2648 for the gas drilling operations uncertainty node 2622 in accordance with an embodiment of the present invention. The inputs 2448 for the node 2622 may include gas drilling operations having N number of inputs from “Gas_drilling_operation_(—)1” to “Gas_drilling_operation_N.” As will be appreciated, in some embodiments the inputs 2448 may include associated probabilities, such as probabilities p_(—)1 through p_N. The inputs 2648 may include different types of gas drilling operations that may be used in an air and gas UBD drilling system. For example, in some embodiments, the inputs 2648 may include: “Gas_drilling_volume_requirements”, “Unloading_the_hole”, “Drying_the_hole”, “Connections”, “Hole_cleaning”, “Well_kicks_detection_and_solution”, “Drilling_with_air”, “Drilling_with_cyrogenic_or_membrance_nitrogen”, “Drilling_with_natural_gas”, and “Mist_drilling”. Additionally, FIG. 26G depicts inputs 2650 for the gas drilling operations recommendations decision node 2624 in accordance with an embodiment of the present invention. The inputs 2650 to the decision node 2624 may include gas drilling operation recommendations and may include N number of inputs from “Gas_drilling_operation_rec_(—)1” to “Gas_drilling_operation_rec_N.” The inputs 2650 may include recommendations, such as recommended practices, for various gas drilling operations, such the gas drilling operations input into the air and gas UBD BDN model 2600.

Finally, FIGS. 26H and 261 depict inputs for the gas drilling rig equipment section 2610 of the model 2600. As shown in FIG. 26H, inputs 2652 to the gas drilling rig equipment uncertainty node 2628 may be gas drilling rig equipment and may include N number of inputs from “Rig_equipment_(—)1” to “Rig_equipment_N.” As will be appreciated, in some embodiments the inputs 2652 may include associated probabilities, such as probabilities p_(—)1 through p_N. The inputs 2652 may include various rig equipment for use in an air and gas UBD system. For example, in some embodiments the inputs 2652 may include “Rotating_head”, “Bit_float_and_string_float”, “Fire_float_and_fire_stop_float”, “Blooie_line”, “Seperators_dedusters_and_mufflers”, “Injected_air_or_gas”, and “Mist_pumps”. FIG. 26I depicts inputs 2654 for the gas drilling rig equipment recommendations decision node 2630 in accordance with an embodiment of the present invention. The inputs 2654 for the decision node 2630 may be gas drilling rig equipment recommendations and may include N number of inputs from “Rig_equipment_rec_(—)1” to “Rig_equipment_rec_N.” The inputs 2654 may include recommendations for gas drilling rig equipment, such as recommended practices, recommended types of equipment, and so on.

As described above, after selecting one or more inputs for the nodes of the different sections 2602, 2604, 2606, and 2608 of the air and gas UBD BDN model 2600, the inputs may be propagated to the consequence nodes 2614, 2620, 2626, and 2632 of each section, and then to the final consequences node 2634, using the Bayesian probability determinations described above in Equations 1, 2, and 4. By using the Bayesian probabilities associate with the inputs, the air and gas UBD BDN model 2600 may provide recommendations or expected utilities at each consequence node. Additionally, the air and gas UBD BDN model 2600 may provide recommendations or expected utilities at the final consequence node 2634 based on the propagated outputs from the consequence nodes 2614, 2620, 2626, and 2632. In some embodiments, the uncertainty nodes of the air and gas UBD BDN model 2600 may have inputs with associated probability distributions. In some embodiments, a user may select an input for one or more uncertainty nodes and view the recommendations based on the propagation of the selected input. For example, a user may select an input for the rotary and hammer drilling uncertainty node 2610 and receive a recommendation (based on the inputs to the rotary and hammer drilling recommendations decision node 2612) at the consequences node 2614. Similarly, a user may select an input for the gas drilling operations uncertainty node 2622 and receive a recommendation (based on the inputs to the gas drilling operations recommendations decision node 2624) from the consequences node 2626. One or multiple sections 2602, 2604, 2606, and 2608 of the air and gas UBD BDN model 2600 may be used; consequently, a user may use one or both sections of the air and gas UBD BDN model 2600 and not use the remaining sections of the air and gas UBD BDN model 2600.

FIGS. 27A and 27B depict selections of inputs and corresponding outputs for the air and gas UBD BDN model 2600 in accordance with an embodiment of the present invention. As depicted in FIG. 27A, a user may select an input for the rotary and hammer drilling uncertainty node 2610, such as a specific rotary or hammer drilling type. As shown in FIG. 27A, a user may select “Horizontal_drilling_with_air_hammers” as the input 2700 for the uncertainty node 2610. The selected input 2700 may be displayed, such as in a dialog box or other user interface element, to indicate the input to the node 2610.

FIG. 27B depicts an example of an output 2702 from the consequences node 2614 based on the input described above in FIG. 27A and in accordance with an embodiment of the present invention. In some embodiments, as shown in FIG. 27B, the output 2702 may be presented as a dialog box displaying the recommendation from the consequences node 2614. For example, the output 2702 from the consequences node 2614 may be based on a determination of a recommendation with the highest Bayesian probability state as determined from inputs received from the decision node 2612 and the selected input 2700 to the uncertainty node 2610. As shown in FIG. 27B, the output 2702 may include text describing details of the recommendation (e.g., “Recommendations text”) for the selected rotary and hammer drilling type input into the model 2600. Accordingly, a user may view recommendations for various inputs to aid in implementation of an air and gas UBD system. In other embodiments, as described above, the output from a BDN model may be provided as a table of expected utility values, a table of Bayesian probability states for each recommendation, or other suitable outputs.

Similarly, FIGS. 28A and 28B depict another selection of inputs and corresponding outputs for the air and gas UBD BDN model 2600 in accordance with an embodiment of the present invention. As depicted in FIG. 28A, a user may select an input 2800 for the gas drilling considerations uncertainty node 2616, such as a specific limit, extreme, challenge or combination thereof encountered in an air and gas UBD system. As shown in FIG. 28A, a user may select “Water_or_wet_holes” as the input 2800 for the uncertainty node 2616. Here again, the selected input 2800 may be displayed, such as in a dialog box or other user interface element, to indicate the input to the node 2616.

As described above, an output from the model 2600 may be provided from a consequences node of the model 2600. FIG. 28B depicts an example of an output 2802 from the consequences node 2620 based on the input described above in FIG. 28A and in accordance with an embodiment of the present invention. The output 2802 may be presented in a dialog box displaying the recommendation from the consequences node 2620. As noted above, the output 2802 may be based on a determination of a recommendation with the highest Bayesian probability state as determined from inputs received from the uncertainty node 2616 and the decision node 2618. As shown in FIG. 28B, the output 2802 may include text describing details of the recommendations (e.g., “Recommendations text”) based on the inputs to the model 2600. Again, a user may view various recommendations for various inputs to aid in implementation of an air and gas UBD system. In other embodiments, as described above, the output from a BDN model may be provided as a table of expected utility values, a table of Bayesian probability states for each recommendation, or other suitable outputs. As will be appreciated, the other sections of the air and gas UBD BDN model 2600 may receive inputs and provide outputs in a similar manner as described above and illustrated FIGS. 27 and 28.

As described above, the UBD expert system may also include a mud cap drilling BDN model for use in determining optimal operations for a mud cap UBD system. FIGS. 29A-29H depict a mud cap drilling BDN model 2900 and associated inputs in accordance with an embodiment of the present invention. As shown in FIG. 29A, the mud cap drilling model 2900 may include three sections: a mud cap drilling types section 2902, a drilling problems section 2904, and a floating mud cap drilling section 2906. The nodes of the various sections are described further below. FIG. 29A also includes connection lines 2908 that indicate the dependencies between the nodes of the mud cap drilling model 2900.

The mud cap drilling types section 2602 includes a mud cap drilling types uncertainty node 2610, a mud cap drilling types recommendations decision node 2612, and a consequences node 2914 that is dependent on the uncertainty node 2610 and the decision node 2612. The drilling problems section 2904 includes a drilling problems uncertainty node 2916, a drilling problems recommendations decision node 2918, and a consequences node 2920 that is dependent on the uncertainty node 2916 and the decision node 2918. Finally, the floating mud cap drilling section 2906 includes a floating mud cap drilling considerations uncertainty node 2922, a floating mud cap drilling recommendations decision node 2924, and a consequences node 2926 that is dependent on the uncertainty node 2922 and the decision node 2924. The output from each of the consequences nodes 2914, 2920, and 2926 may be propagated to a final consequences node 2928 and a UBD expert node 2630. Thus, the final consequences node is dependent on the consequences nodes 2914, 2920, and 2926 of each section of the mud cap UDB BDN model 2900.

In some embodiments, as described above with regard to the other BDN models discussed herein, the mud cap UDB BDN model 2900 may be implemented in a user interface similar to the depiction of the model 2900 in FIG. 29A. In such embodiments, for example, each node of the model 2900 may include a button 2932 that enables a user to select a value for the node or see the determinations performed by a node. For example, as described below, a user may select (e.g., click) the button 2932A to select a mud cap drilling types input for the model 2900. Similarly, a user may select the button 2932D to select an input for the drilling problems uncertainty node 2916, the button 2932G to select an input for the floating mud cap drilling considerations uncertainty node 2922, and so on. As noted above, evidence (inputs) may be introduced at any nodes of the model 2900 and propagated throughout the model 2900 using the Bayesian logic described above.

FIGS. 29B-29H depict the inputs for each node of the mud cap UBD BDN model 2900 in accordance with an embodiment of the present invention. In some of these figures, the section delineations and some reference numerals may be omitted for clarity. FIGS. 29B and 29C depict the inputs for the mud cap drilling types section 2902 of the mud cap UBD BDN model 2900. FIG. 29B depicts inputs 2934 for the mud cap drilling types uncertainty node 2910 in accordance with an embodiment of the present invention. The inputs 2934 to the uncertainty node 2910 may include N number of inputs from “mud_cap_drilling_(—)1” to “mud_cap_drilling_N.” As will be appreciated, in some embodiments the inputs 2934 may include associated probabilities, such as probabilities p_(—)1 through p_N. The input 2934 may include different mud cap drilling types that may be used in a UBD system and may include, for example: “Mud_cap_construction”, “Pressure_mud_cap”, “PMCD_total_losses_applicability_test”, “Connections_with_PCMD”, and “Trips_with_pressurized_mud_caps”.

FIG. 29C depicts inputs 2936 for the mud cap drilling types recommendations decision node 2912 in accordance with an embodiment of the present invention. The inputs 2936 to the decision node 2912 may include recommendations and may include N number of inputs from “Mud_cap_drilling_rec_(—)1” to “Mud_cap_drilling_rec_N.” Such inputs may include recommendations, such as recommended practices, for types of mud cap drilling operations.

Next, FIGS. 29D and 29E depict inputs for the nodes of the drilling problems section 2904. FIG. 29D depicts inputs 2938 for the drilling problems uncertainty node 2916 in accordance with an embodiment of the present invention. The inputs 2938 to the drilling problems uncertainty node 2916 may be drilling problems 2938 and may include N number of inputs from “drilling_problem_(—)1” to “drilling_problem_N.” As will be appreciated, in some embodiments the inputs 2938 may include associated probabilities, such as probabilities p_(—)1 through p_N. The inputs 2938 may include various problems that may be encountered in a mud cap UBD system. For example, in some embodiments the inputs 2938 may include “Drilling_with_a_static_overbalanced”, “Drilling_ahead_with_mud_losses”, “Constant_bottom_hole_pressure”, and “Horizontal_wells”. FIG. 29E depicts inputs 2940 for the drilling problems recommendations decision node 2918 in accordance with an embodiment of the present invention. As shown in FIG. 29E, the inputs 2940 may be drilling problem recommendations 2940 and may include N number of inputs from “drilling_problem_rec_(—)1” to “drilling_problem_rec_N.” The inputs 2940 may include recommendations, such as recommended practices, for addressing the drilling problems of a mud cap UBD system.

FIGS. 29F and 29G depict inputs for nodes of the floating mud cap drilling section 2906. FIG. 29F depicts inputs 2942 for the uncertainty node 2922 of the floating mud cap drilling section 2906 in accordance with an embodiment of the present invention. The inputs 2942 for the floating mud cap drilling considerations uncertainty node 2922 may be floating mud cap drilling types and may include N number of inputs from “floating_mud_cap_(—)1” to “floating_mud_cap_N.” As will be appreciated, in some embodiments the inputs 2942 may include associated probabilities, such as probabilities p_(—)1 through p_N. These inputs may include considerations for floating mud cap operations. In some embodiments, for example, the inputs 2942 may include: “Water_availability”, “Fluid_level_measurement”, “Continuous_annular_injection_FMCD”, and “Water_sensitive_formations_exposed.” Finally, FIG. 29G depicts inputs 2944 for the decision node 2924 of the floating mud cap drilling section 2906 in accordance with an embodiment of the present invention. As shown in FIG. 29G, the inputs 2944 may be input into the model 2900 and may include N number of inputs from “floating_mud_cap_rec_(—)1” to “floating_mud_cap_rec_N.” The inputs 2944 may include recommendations, such as recommended practices, for operating a floating mud cap UBD drilling system, such as in a depleted formation.

As described above, after selecting one or more inputs for the nodes of the different sections 2902, 2904, and 2906 of the mud cap UBD BDN model 2900, the inputs may be propagated to the consequence nodes 2914, 2920, and 2926 of each section, and then to the final consequences node 2928, using the Bayesian probability determinations described above in Equations 1, 2, and 4. By using the probability associate with the inputs, the mud cap UDB BDN model 2900 may then provide recommendations or expected utilities at each consequence node 2914, 2920, and 2926. Additionally, the mud cap UDB BDN model 2900 may provide recommendations or expected utilities at the final consequence node 2928 based on the propagated outputs from the consequence nodes 2914, 2920, and 2926. In some embodiments, the uncertainty nodes of the mud cap UDB BDN model 2900 may have inputs with associated probability distributions. In some embodiments, a user may select an input for one or more uncertainty nodes and view the recommendations based on the propagation of the selected input. For example, a user may select an input for the mud cap background uncertainty node 2910 and receive a recommendation (based on the inputs to the mud cap background recommendations decision node 2912) at the consequences node 2914. Similarly, a user may select an input for the drilling problems uncertainty node 2916 and receive a recommendation (based on the inputs to the drilling problems recommendations decision node 2918) from the consequences node 2920. Here again, one or multiple sections 2902, 2904, and 2906 of the mud cap UDB BDN model 2900 may be used; consequently, a user may use one or both sections of the mud cap UDB BDN model 2900 and not use the remaining sections of the mud cap UDB BDN model 2900.

FIGS. 30A and 30B depict selections of inputs and corresponding outputs for the mud cap UBD BDN model 2900. As described above, a user may select inputs for nodes of the mud cap UBD BDN model 2900 and receive outputs from the consequences nodes based on propagation of the inputs in the model 2900. For example, as depicted in FIG. 30A, a user may select an input 3000 for the mud cap drilling types uncertainty node 2910 and in accordance with an embodiment of the present invention. As shown in FIG. 30A, a user may select “Trips_with_pressurized_mud_caps” for the uncertainty node 2910 and the input 3000 may be displayed, such as in a dialog box or other user interface element.

FIG. 30B depicts an example of the output from the consequences node 2914 of the mud cap drilling types section 2902 in accordance with an embodiment of the present invention. As shown in FIG. 30B, in some embodiments an output 3002 may be provided as a dialog box displaying the recommendation from the consequences node 2914. For example, the output 2902 may be based on a determination of a recommendation with the highest Bayesian probability state as determined from inputs received from the uncertainty node 2910 and the decision node 2912. In some embodiments, as shown in FIG. 30B, the output 3002 may be provided as a dialog box and may include text describing details of the recommendations (e.g., “Recommendations text”). Accordingly, a user may view recommendations for various inputs to aid in implementation of a mud cap UBD system. In other embodiments, as described above, the output from a BDN model may be provided as a table of expected utility values, a table of Bayesian probability states for each recommendation, or other suitable outputs.

Additionally, FIGS. 31A and 31B depict another selection of inputs and corresponding outputs for mud cap UBD BDN model 2900 in accordance with an embodiment of the present invention. As shown in FIG. 31A, a user may select an input 3100 for the drilling problems uncertainty node 2916 of the drilling problems section 2904, such a specific drilling problem encountered in a mud cap UBD BDN model 2900. As shown this figure, a user may select “Drilling_ahead_with_mud_losses” as the input 3100 for the uncertainty node 2916.

FIG. 31B depicts an example of an output 3102 from the consequences node 2920 based on the input described above and depicted in FIG. 31A, and in accordance with an embodiment of the present invention. Here again, the output 3102 may be provided in a dialog box that displays the recommendation from the consequences node 2920. Here again, the output 3102 may be based on a determination of a recommendation with the highest Bayesian probability state as determined from inputs received from the uncertainty node 2916 and the decision node 2918. For example, as shown in FIG. 31B, the output 3102 may include text describing details of the drilling problems recommendations (e.g., “Recommendations text”) for the selected input 3100 entered into the model 2900. In other embodiments, as described above, the output from a BDN model may be provided as a table of expected utility values, a table of Bayesian probability states for each recommendation, or other suitable outputs. As will be appreciated, the other sections of the flow UBD BDN model 2900 may receive inputs and provide outputs in a similar manner as described above and illustrated FIGS. 30 and 31.

Further, the UBD expert system may also include an underbalanced liner drilling (UBLD) BDN model for use in determining optimal operations in a UBLD system. FIGS. 32A-32G depict a UBLD BDN model 3200 and associated inputs in accordance with an embodiment of the present invention. The UBLD BDN model 3200 may include three sections, the nodes of which are described below: a UBLD plans section 3202, a UBLD advantages and problems 3204, and a UBLD considerations section 3206. FIG. 32A also includes connection lines 3208 that indicate the dependencies between the nodes of the UBLD BDN model 3200.

Each section of the UBLD BDN model 3200 is described further below. The UBLD plans section 3202 includes a UBLD plans uncertainty node 3210, a UBLD plans recommendations decision node 3212, and a consequences node 3214 that is dependent on the uncertainty node 3210 and the decision node 3212. The UBLD problems and advantages section 3204 includes a UBLD solvable problems uncertainty node 3216, a UBLD advantages decision node 3218, and a consequences node 3220 that is dependent on the uncertainty node 3216 and the decision node 3218. Additionally, the considerations section 3206 includes a UBLD considerations uncertainty node 3222, a UBLD considerations recommendations decision node 3224, and a consequences node 3226 that is dependent on the uncertainty node 3222 and the decision node 3224. The output from each of the consequences nodes 3214, 3220, and 3226 may be propagated to a final consequences node 3228 and a UBD expert system node 3220. Accordingly, the final consequences node 3228 is dependent on the consequences nodes 3214, 3220, and 3226 for each section model 3200.

In some embodiments, as described above in the other BDN models discussed herein, the UBLD BDN model 3200 may be implemented in a user interface similar to the depiction of the model 3200 in FIG. 32A. In such embodiments, for example, each node of the model 3200 may include a button 3232 that enables a user to select a value for the node or see the determinations performed by a node. For example, as described below, a user may select (e.g., click) the button 3232A to select a UBLD plans input for the model 3200. Similarly, a user may select the button 3232D to select an input for the UBLD solvable problems uncertainty node 3216, and so on. As noted above, evidence (inputs) may be introduced at any nodes of the model 3200 and propagated throughout the model 3200 using the Bayesian logic described above.

FIGS. 32B-32G depict the inputs for each node of the UBLD BDN model 3200 in accordance with an embodiment of the present invention. In some of these figures, the section delineations and some reference numerals may be omitted for clarity. FIGS. 32B and 32C depict the inputs for the UBLD plans section 3202 of the model. Accordingly, FIG. 32B depicts inputs 3234 for the UBLD plans uncertainty node 3210 in accordance with an embodiment of the present invention. The inputs 3234 to the uncertainty node 3210 may include N number of inputs from “UBLD_plan_(—)1” to “UBLD_plan_N.” As will be appreciated, in some embodiments the inputs 3243 may include associated probabilities, such as probabilities p_(—)1 through p_N. The inputs 3243 may include plans for implementing a UBLD system or any other plans associated with a UBLD system. For example, in some embodiments the selectable UBLD plans may include: “The_bit”, “Hydraulic_design”, and “Torsional_limits”. Additionally, FIG. 32C illustrates inputs 3236 for the UBLD plans recommendations decision node 3212 in accordance with an embodiment of the present invention. The inputs 3236 to the decision node 3212 may include plan recommendations and may include N number of inputs, as shown by inputs “UBLD_basic_plan_rec_(—)1” to “UBLD_basic_plan_rec_N.” The inputs 3236 may include recommendations, such as recommended practices, for various UBLD plans.

Additionally, FIGS. 32D and 32E depict the inputs for the problems and advantages section 3204 of the UBLD BDN model 3200. FIG. 32D depicts inputs 3238 for the UBLD solvable problems uncertainty node 3216 in accordance with an embodiment of the present invention. The inputs to the uncertainty node 3216 may include N number of problems from “UBLD_problem_(—)1” to “UBLD_problem_N.” As will be appreciated, in some embodiments the inputs 3238 may include associated probabilities, such as probabilities p_(—)1 through p_N. The inputs 3238 may include problems that are solvable via the implementation of a UBLD system. For example, such problems may include “Dual_pressure_zones”, “Differential_sticking”, “Wellbore_ballooning”, “Cementing_the_liner”, “No_obvious_depth”, “Hole_size_limits”, and “Casing_centralization”and_stabilization”. Next, FIG. 32E depicts the inputs for the UBLD advantages decision node 3218 in accordance with an embodiment of the present invention. As shown in FIG. 32E, the inputs 3240 may include N number of inputs from “UBLD_advantage_(—)1” to “UBLD_advantage_N.” The inputs 3240 may include various advantages of a UBLD system, such as advantages of a UBLD system over a conventional UBD system.

Finally, FIGS. 32F and 32G depict the inputs for the UBLD considerations section 3206 of the UBLD BDN model 3200. Thus, FIG. 32F depicts inputs 3242 for the UBLD considerations uncertainty node 3222 in accordance with an embodiment of the present invention. The inputs 3242 to this node may include N number of inputs, e.g., “UBLD_considerations_(—)1” to “UBLD considerations_N.” As will be appreciated, in some embodiments the inputs 3242 may include associated probabilities, such as probabilities p_(—)1 through p_N. The UBLD inputs 3242 may include considerations, such as limits, challenges, and the like, to implementing and operating a UBLD system. For example, in some embodiments such considerations may include, for example, “Bit_requirements”, “Liner_availability”, “Liner_hanger”, “Well_control_considerations”, and “Drilling_fluid_considerations”. Similarly, FIG. 32G depicts inputs 3244 for the UBLD considerations requirements decision node 3224 in accordance with an embodiment of the present invention. The inputs 3244 to the decision node 3224 may be requirements for a UBLD system to address the considerations of a UBLD system, such as the considerations input for the uncertainty node 3222. Accordingly, the inputs 3244 may include N number of inputs from “UBLD_rec_(—)1” to “UBLD_rec_N.”

As described above, after selecting one or more inputs for the nodes of the different sections 3202, 3204, and 3206 of the UBLD BDN model 3200, the inputs may be propagated to the consequence nodes 3214, 3220, and 3226 of each section, and then to the final consequences node 3228, using the Bayesian probability determinations described above in Equations 1, 2, and 4. By using the Bayesian probabilities associate with the inputs, the UBLD BDN model 3200 may provide recommendations or expected utilities at each consequence node. Additionally, the UBLD BDN model 3200 may provide recommendations or expected utilities at the final consequence node 3228 based on the propagated outputs from the consequence nodes 3214, 3220, and 3226. In some embodiments, the uncertainty nodes of the UBLD BDN model 3200 may have inputs with associated probability distributions. In some embodiments, a user may select an input for one or more uncertainty nodes and view the recommendations based on the propagation of the selected input. For example, a user may select an input for the UBLD plans uncertainty node 3210 and receive a recommendation (based on the inputs to the UBLD plans recommendations decision node 3212) at the consequences node 3214. Similarly, a user may select an input for the UBLD problems uncertainty node 3216 and receive a recommendation (based on the inputs to the UBLD advantages decision node 3218) from the consequences node 3220. One or multiple sections 3202, 3204, and 3206 of the UBLD BDN model 3200 may be used; thus, a user may use one or multiple sections of the UBLD BDN model 3200 and not use the remaining sections of the UBLD BDN model 3200.

FIGS. 33A and 33B depict selections of inputs and corresponding outputs for the UBLD BDN model 3200 in accordance with an embodiment of the present invention. As described above, a user may select inputs for nodes of the UBLD BDN model 3200 and receive outputs from the consequences nodes based on propagation of the inputs in the model 3200. As depicted in FIG. 33A, for example, a user may select an input 3300 for the UBLD plans uncertainty node 3210. As shown in FIG. 32A, a user may select “The_bit” as the input for the uncertainty node 3210 and the inputs 3300 may be displayed, such as in a dialog box or other user interface element.

FIG. 33B depicts an example of an output 3202 from the consequences node 3214 of the UBLD BDN model 3200 in accordance with an embodiment of the present invention. As shown in FIG. 33B, the output 3202 may be provided as a dialog box that displays the recommendation from the consequences node 3214. For example, the output 3202 from the consequences node 3214 may be based on a determination of a recommendation with the highest Bayesian probability state as determined from inputs received from the decision node 3212 and the selected input 3200 to the uncertainty node 3210. The output 3202 may include text describing the recommendation (e.g., “Recommendations text) for the selected input 3000. Thus, a user may view recommendations for various inputs to aid in implementation of a UBLD system. In other embodiments, as described above, the output from a BDN model may be provided as a table of expected utility values, a table of Bayesian probability states for each recommendation, or other suitable outputs.

FIGS. 34A and 34B depict another example of another selected input and corresponding outputs from the UBLD BDN model 3200 in accordance with an embodiment of the present invention. As shown in FIG. 34A, a user may select an input 3400 for the UBLD solvable problems uncertainty node 3216. Here again, in some embodiments the input may be displayed in a dialog box or other user interface element. As shown in FIG. 34A, the selected input 3400 for the uncertainty node 3216 may be “Wellbore_ballooning”. Next, FIG. 34B depicts an output 3402 from the consequences node 3220 in accordance with an embodiment of the present invention. The output 3402 may be provided in a dialog box or other user interface element that displays the recommendation from the consequences node 3220. As noted above, the output 3202 may be based on a determination of a recommendation with the highest Bayesian probability state as determined from inputs received from the uncertainty node 3216 and the decision node 3218. As shown in FIG. 34B, the output may include text describing the UBLD advantages (e.g., advantages text) for the selected problem solved by UBLD input to the uncertainty node 3216. In other embodiments, as described above, the output from a BDN model may be provided as a table of expected utility values, a table of Bayesian probability states for each recommendation, or other suitable outputs. As will be appreciated, the other sections of the UBLD BDN model 3200 may receive inputs and provide outputs in a similar manner as described above and illustrated FIGS. 33 and 34.

In some embodiments, a UBD expert system may include a BDN model for an underbalanced coil tube (UBCT) system for use in determining optimal operations for a UBCT drilling system. FIGS. 35A-35E depict a UBCT BDN model 3500 and inputs for the various nodes of the model 3500 in accordance with an embodiment of the present invention. As shown in FIG. 35A, the UBCT BDN model 3500 may include a preplanning section 3502 and a UBCT considerations section 3504. The nodes of the sections 3502 and 3504 are described further below. FIG. 35A also depicts connection lines 3505 that indicate the dependencies between the nodes of the UBCT model 3500.

In some embodiments, as described above in the other BDN models discussed herein, the UBCT drilling BDN model 3500 may be implemented in a user interface similar to the depiction of the model 3500 in FIG. 35A. In such embodiments, for example, each node of the model 3500 may include a control 3522 that enables a user to select a value for the node or see the determinations performed by a node. For example, as described below, a user may select (e.g., click) the control 3522A to select a preplanning input for the preplanning uncertainty node 3506. Similarly, a user may select the control 3522D to select an input for the UBCT drilling considerations uncertainty node 3512, and so on. As noted above, evidence (inputs) may be introduced at any nodes of the model 3500 and propagated throughout the model 3500 using the Bayesian logic described above.

The preplanning section 3502 includes a preplanning uncertainty node 3506, preplanning requirements decision node 3508, and a consequences node 3510 dependent on the uncertainty node 3506 and the decision node 3508. Additionally, the drilling considerations section 3504 includes a UBCT drilling considerations uncertainty node 3512, a UBCT drilling considerations solutions decision node 3514, and a consequences node 3516 dependent on the uncertainty node 3512 and the decision node 3514. The output from the consequences nodes 3510 and 3516 may be propagated to a final consequences node 3518 and a UBD expert system node 3520. Thus, the final consequences node 3518 is dependent on the consequences nodes 3510 and 3516.

FIGS. 35B-35E depict the inputs for each node of the UBCT BDN model 3500 in accordance with an embodiment of the present invention. In some of these figures, the section delineations and some reference numerals may be omitted for clarity. FIGS. 35B and 35C depict the inputs for the preplanning section 3502. FIG. 35B depicts inputs 3524 for the preplanning uncertainty node 3506 in accordance with an embodiment of the present invention. The inputs 3524 to the uncertainty node 3506 may be UBCT preplans and may include N number of inputs from “UCTCD_preplan_(—)1” to “UCTCD_preplan_(—)2.” As will be appreciated, in some embodiments the inputs 3524 may include associated probabilities, such as probabilities p_(—)1 through p_N. The inputs 3524 may include plans for preparation (i.e., preplans) of a UBCT drilling system. For example, in some embodiments, the inputs 3524 may include” “Candidate_selection”, “Pressure_categories_and_BOP_stack_requirement” and “Coiled_tubing_mechanical_considerations.” Next, FIG. 35C depicts inputs 3526 for the preplanning requirements decision node 3508 in accordance with an embodiment of the present invention. The inputs 3526 to the decision node 3508 may be preplanning requirements and may include N number of inputs from “UBCT_preplan_req_(—)1” to “UBCT_preplan_req_N.” The inputs 3526 may include detailed requirements for different preplanning considerations input into the UBCT BDN model 3500.

FIGS. 35D and 25E depict the inputs for the UBCT drilling considerations section 3504. For example, FIG. 35D depicts inputs 3528 for the UBCT drilling considerations uncertainty node 3512 in accordance with an embodiment of the present invention. The inputs 3528 may be UBCT drilling considerations and may include N number of inputs from “UBCT_consideration_(—)1” to “UBCT_consideration_N.” As will be appreciated, in some embodiments the inputs 3512 may include associated probabilities, such as probabilities p_(—)1 through p_N. In some embodiments, the UBCT drilling considerations may include challenges, limits, and so on associated with UBCT drilling systems. The inputs 3528 may include considerations that may be encountered when implementing and operating a UBCT drilling system. For example, in some embodiments the inputs 3528 may include “ROP_reduction”, “Wellhead_or_downhole_annulus_pressure”, “Surface_injection_pressure”, “Downhole_tubing_pressure”, and “Drill_into_fracture.”

FIG. 35E depicts inputs 3530 for the UBCT drilling considerations solutions decision node 3514 in accordance with an embodiment of the present invention. The inputs to the decision node 3514 may include N number of inputs from “UBCT_solution_(—)1” to UBCT_solution_N.” The inputs 3530 may include solutions to considerations that may be encountered in a UBCT drilling system, such as the considerations input into the model 3500.

As described above, after selecting one or more inputs for the nodes of the different sections 3502 and 3504 of the UBCTD BDN model 3500, the inputs may be propagated to the consequence nodes 3510 and 3516 of each section, and then to the final consequences node 3518, using the Bayesian probability determinations described above in Equations 1, 2, and 4. By using the probably states associate with the inputs, the UBCTD BDN model 3500 may then provide recommendations or expected utilities at each consequence node 3510 and 3516. Additionally, the UBCTD BDN model 3500 may provide recommendations or expected utilities at the final consequence node 3518 based on the propagated outputs from the consequence nodes 3510 and 3516. In some embodiments, the uncertainty nodes of the UBCTD BDN model 3500 may have inputs with associated probability distributions. In some embodiments, a user may select an input for one or more uncertainty nodes and view the recommendations based on the propagation of the selected input. For example, a user may select an input for the preplanning uncertainty node 3506 and receive a recommendation (based on the inputs to the preplanning requirements decision node 3508) at the consequences node 3510. Similarly, a user may select an input for the foam systems design uncertainty node 3512 and receive a recommendation (based on the inputs to the UBCT drilling considerations decision node 3514) from the consequences node 3516. One or both sections 3502 and 3504 of the UBCTD BDN model 3500 may be used; consequently, a user may use one or both sections of the UBCTD BDN model 3500 and not use the remaining sections of the flow UDB BDN model 2400

FIGS. 36A and 36B depict the selection of inputs and the corresponding outputs for the UBCTD BDN model 3500 in accordance with an embodiment of the present invention. As mentioned above, a user may select inputs for one or nodes of the UBCTD BDN model 3500 and receive output from the consequences node as the inputs are propagated in the model 3500. For example, as shown in FIG. 36A, a user may select an input 3600 for the preplanning uncertainty node 3506. As depicted in FIG. 36A, a user may select “Pressure_categories_and_BOP_stack_requirements” as the input 3600 for the uncertainty node 3506. In some embodiments, the input 3600 may be displayed in a dialog box or other user interface element to indicate the input to a selected node 3506.

FIG. 36B thus depicts an output 3602 from the consequences node 3510 of the UBCTD model 3500 based on the input described above and in accordance with an embodiment of the present invention. For example, the output 3602 may be provided in a dialog box or other user interface element that displays the recommendation from the consequences node 3510. The output 3502 may be based on a determination of a recommendation with the highest Bayesian probability state as determined from inputs received from the uncertainty node 3506 and the decision node 3508. As shown in FIG. 36B, in some embodiments the output 3602 may include text describing the recommendation (e.g., Recommendations text) output from the consequences node 3510. Accordingly, a user may view recommendations for various inputs to aid in implementation of a UBCT drilling system. In other embodiments, as described above, the output 3602 from a BDN model may be provided as a table of expected utility values, a table of Bayesian probability states for each recommendation, or other suitable outputs. As will be appreciated, the other section of the UBCTD BDN model 3500 may receive inputs and provide outputs in a similar manner as described above and illustrated FIGS. 36A and 36B.

Finally, in some embodiments the UBD expert system may include a snubbing and stripping BDN model for use in determining optimal snubbing and stripping operations for a UBD system. FIGS. 37A-37I depict a snubbing and stripping BDN model 3700 in accordance with an embodiment of the present invention. The snubbing and stripping BDN model 3700 includes four sections: a snubbing section 3702, a snubbing units section 3704, a snubbing operations procedure section 3706, and a stripping procedures section 3708. The nodes of each section are described further below. FIG. 37A also depicts connection lines 3709 that indicate the dependencies between the nodes of the model 3700.

Each section of the snubbing and stripping BDN model 3700 is described in detail below. The snubbing section 3702 includes a snubbing types uncertainty node 3710, a snubbing types recommendations decision node 3712, and a consequences node 3714 that depends on the uncertainty node 3710 and the decision node 3712. Additionally, the snubbing units section 3704 includes a snubbing units uncertainty node 3716, a snubbing units recommendations decision node 3718, and a consequences node 3720 that depends on the uncertainty node 3716 and the decision node 3718. The snubbing operations section 3706 includes a snubbing operations uncertainty node 3722, a snubbing operations recommendations decision node 3724, and a consequences node 3726 that depends on the uncertainty node 3722 and the decision node 3724. Finally, the stripping procedures section 3708 includes a general stripping procedures uncertainty node 3728, a general stripping procedures recommendations decision node 3730, and a consequences node 3732 that depends on the uncertainty node 3728 and the decision node 3730. The output from each of the consequences nodes 3714, 3720, 3726, and 3732 may be propagated to a final consequences node 3734 and a UBD expert system node 3736. Accordingly, the final consequences node 3734 is dependent on the consequences nodes 3714, 3720, 3726, and 3732 for each section of the model 3700.

In some embodiments, as described above in the other BDN models discussed herein, the snubbing and stripping BDN model 3700 may be implemented in a user interface similar to the depiction of the model 3700 in FIG. 37A. In such embodiments, for example, each node of the model 3700 may include a control 3738 that enables a user to select a value for the node or see the determinations performed by a node. For example, as described below, a user may select (e.g., click) the control 3738A to select an input for the snubbing types uncertainty node 3710. Similarly, a user may select the control 3738D to select an input for the snubbing units uncertainty node 3716, and so on. As noted above, evidence (inputs) may be introduced at any nodes of the model 3700 and propagated throughout the model 3700 using the Bayesian logic described above.

FIGS. 37B-37I depict the inputs for each node of the snubbing and stripping model 3700 in accordance with an embodiment of the present invention. In some of these figures, the section delineations and some reference numerals may be omitted for clarity. FIGS. 37B and 37C depict the inputs for the snubbing section 3702. Accordingly, FIG. 37B depicts inputs 3740 for the snubbing types uncertainty node 3710 in accordance with an embodiment of the present invention. The inputs may be snubbing types and may include N number of inputs from “Snubbing_(—)1” to “Snubbing_N.” As will be appreciated, in some embodiments the inputs 3740 may include associated probabilities, such as probabilities p_(—)1 through p_N. The inputs 3740 may include basic considerations for implementing a snubbing operation. For example, in some embodiments the inputs 3740 may include: “Hydraulic_system”, “Stripping_ram_to_ram”, “Stripping_with_annular_preventer_or_stripping_rubber”, “Pipe_light”, “Pipe_heavy”, and “Fluid_flow”.

FIG. 37C depicts inputs 3742 for the snubbing types recommendations decision node 3712 in accordance with an embodiment of the present invention. The inputs 3742 may be selectable snubbing recommendations and may include N number of inputs from “basic_snubbing_rec_(—)1” to “basic_snubbing_rec_N.” The inputs 3742 may include detailed recommendations for various snubbing types, such as the considerations input into the uncertainty node 3710.

Next, FIGS. 37D and 37E depicts the inputs for the snubbing units section 3704. Accordingly, FIG. 37D depicts inputs 3744 for the snubbing units uncertainty node 3716 in accordance with an embodiment of the present invention. The inputs 3744 to the uncertainty node 3716 may be snubbing units and may include N number of inputs from “snubbing_unit_(—)1” to “snubbing_unit_N.” As will be appreciated, in some embodiments the inputs 3744 may include associated probabilities, such as probabilities p_(—)1 through p_N. The inputs 3744 may include the units used in a snubbing operation and, in some embodiments, may include the following: “Basic_snubbing_unit”, “Work_string_and_components”, “Well_control”, and “Auxiliary_equipment”. Additionally, FIG. 37E depicts inputs 3746 for the snubbing units recommendations decision node 3718 in accordance with an embodiment of the present invention. As shown in FIG. 37E, the inputs 3746 may be snubbing units recommendations and may include N number of inputs from “snubbing_unit_rec_(—)1” to “snubbing_unit_rec_N.” The inputs 3746 may include detailed recommendations for using a particular snubbing unit, such as the units input into the uncertainty node 3716.

Further, FIGS. 37F and 37G depict inputs for the snubbing operations section 3706. FIG. 37F thus depicts inputs 3748 for the snubbing operations uncertainty node 3712 in accordance with an embodiment of the present invention. As shown in FIG. 37F, the inputs 3748 may be snubbing operations and may include N number of inputs from “snubbing_operation_(—)1” to “snubbing_operation_N.” As will be appreciated, in some embodiments the inputs 3748 may include associated probabilities, such as probabilities p_(—)1 through p_N. The inputs 3748 may be different types of snubbing operations and may include, for example: “Temporary_securing_of_the_well”, “Lubrication”, and “Shear_or_connect_disconnect_in_BOP_stack_lubrication.” Additionally, FIG. 37G depicts inputs 3750 for the snubbing operations recommendations decision node 3714 in accordance with an embodiment of the present invention. The inputs 3750 may be snubbing operation recommendations and may include N number of inputs from “snubbing_operation_rec_(—)1” to “snubbing_operation_N.” The inputs 3750 may include detailed recommendations for different snubbing operations, such as the snubbing operations input for the snubbing units uncertainty node 3716.

Finally, FIGS. 37H and 371 depict the inputs for the general stripping procedures section 3708 of the snubbing and stripping BDN model 3700. FIG. 37H depicts the inputs for the general stripping procedures uncertainty node 3718 in accordance with an embodiment of the present invention. As shown in FIG. 37H, inputs 3752 to the uncertainty node 3718 may be stripping procedures and may include N number of inputs from “stripping_proc_(—)1” to “stripping_proc_N.” As will be appreciated, in some embodiments the inputs 3752 may include associated probabilities, such as probabilities p_(—)1 through p_N. The inputs 3752 may include general stripping procedures for use in UBD system. For example, in some embodiments the inputs 3752 may include: “Packoff_stripper_rubber”, “Packoff_annular_BOP”, “Annular_to_ram”, and “Ram_to_ram.” Next, FIG. 37I depicts inputs 3754 for the stripping procedures recommendations decision node 3730 in accordance with an embodiment of the present invention. The inputs 3754 to the decision node 3730 may be stripping procedure recommendations and may include N number of inputs from “Stripping_proc_rec_(—)1” to “Stripping_proc_rec_N.” The inputs 3754 may include detailed recommendations for various stripping procedures, such as the stripping procedures input for the general stripping procedures uncertainty node 3718.

As described above, after selecting one or more inputs for the nodes of the different sections 3702, 3704, 3706, and 3708 of the snubbing and stripping BDN model 3700, the inputs may be propagated to the consequence nodes 3714, 3720, 3726, and 2632 of each section, and then to the final consequences node 3734, using the Bayesian probability determinations described above in Equations 1, 2, and 4. By using the Bayesian probabilities associate with the inputs, the snubbing and stripping BDN model 3700 may provide recommendations or expected utilities at each consequence node. Additionally, the snubbing and stripping BDN model 3700 may provide recommendations or expected utilities at the final consequence node 3734 based on the propagated outputs from the consequence nodes 3714, 3720, 3726, and 2632. In some embodiments, the uncertainty nodes of the snubbing and stripping BDN model 3700 may have inputs with associated probability distributions. In some embodiments, a user may select an input for one or more uncertainty nodes and view the recommendations based on the propagation of the selected input. For example, a user may select an input for the rotary and hammer drilling uncertainty node 3710 and receive a recommendation (based on the inputs to the rotary and hammer drilling recommendations decision node 3712) at the consequences node 3714. Similarly, a user may select an input for the gas drilling operations uncertainty node 3722 and receive a recommendation (based on the inputs to the gas drilling operations recommendations decision node 3724) from the consequences node 3726. One or multiple sections 3702, 3704, 3706, and 3708 of the snubbing and stripping BDN model 3700 may be used; consequently, a user may use one or both sections of the snubbing and stripping BDN model 3700 and not use the remaining sections of the snubbing and stripping BDN model 3700.

FIGS. 38A and 38B depict selections of inputs and corresponding outputs for the snubbing and stripping BDN model 3700 in accordance with an embodiment of the present invention. As depicted in FIG. 37A, a user may select an input for the snubbing types uncertainty node 3710, such as a snubbing type. As shown in FIG. 38A, a user may select “Stripping_with_annular_preventer_or_stripping_rubber” as the input 3800 for the uncertainty node 3810. The selected input 3800 may be displayed, such as in a dialog box or other user interface element, to indicate the input to the node 3810.

FIG. 38B depicts an example of an output 3802 from the consequences node 3714 based on the input described above in FIG. 38A and in accordance with an embodiment of the present invention. In some embodiments, as shown in FIG. 38B, the output 3802 may be presented as a dialog box displaying the recommendation from the consequences node 3714. For example, as described above, the output 3802 from the consequences node 3714 may be based on a determination of a recommendation with the highest Bayesian probability state as determined from inputs received from the decision node 3712 and the selected input 3800 to the uncertainty node 3710. As shown in FIG. 38B, the output 3802 may include text describing details of the recommendation (e.g., “Recommendations text”) for the selected rotary and hammer drilling type input into the model 3700. Accordingly, a user may view recommendations for various inputs to aid in implementation of an air and gas UBD system. In other embodiments, as described above, the output from a BDN model may be provided as a table of expected utility values, a table of Bayesian probability states for each recommendation, or other suitable outputs.

Similarly, FIGS. 39A and 39B depict another selection of inputs and corresponding outputs for the snubbing and stripping BDN model 3700 in accordance with an embodiment of the present invention. As depicted in FIG. 39A, a user may select an input 3900 for the snubbing units uncertainty node 3716, such as a snubbing units used in snubbing operation in a UBD system. As shown in FIG. 39A, a user may select “Auxiliary_equipment” as the input 3900 for the uncertainty node 3716. Here again, the selected input 3900 may be displayed, such as in a dialog box or other user interface element, to indicate the input to the node 37161

As described above, an output from the model 3700 may be provided from a consequences node of the model 3700. FIG. 39B depicts an example of an output 3902 from the consequences node 3720 based on the input described above in FIG. 39B and in accordance with an embodiment of the present invention. As noted above, the output 3902 may be presented in a dialog box displaying the recommendation from the consequences node 3720. As noted above, the output 3902 may be based on a determination of a recommendation with the highest Bayesian probability state as determined from inputs received from the uncertainty node 3716 and the decision node 3718. As shown in FIG. 39B, the output 3902 may include text describing details of the recommendations (e.g., “Recommendations text”) based on the inputs to the model 3700. Again, a user may view various recommendations for various inputs to aid in implementation of an air and gas UBD system. In other embodiments, as described above, the output from a BDN model may be provided as a table of expected utility values, a table of Bayesian probability states for each recommendation, or other suitable outputs. As will be appreciated, the other sections of the air and gas UBD BDN model 3700 may receive inputs and provide outputs in a similar manner as described above and illustrated FIGS. 38 and 39.

The various BDN models described above may be constructed based on the inputs for the uncertainty nodes, decision nodes, and the associated probabilities. The construction of a section of the various BDN models is illustrated in FIG. 40. FIG. 40 depicts a process 4000 illustrating the construction of a section of a BDN model in accordance with an embodiment of the present invention. The process 4000 depicts the construction of a section having an uncertainty node, a decision node, and a consequences node, arranged in the manner described above. For example, the inputs to an uncertainty node may be determined (block 4002). The inputs for an uncertainty node of a particular section of a specific BDN model may determined from expert data 4004. For example, in some embodiments expert data may be obtained from various sources, such as consultations with experts, scientific literature, expert reports, and the like. The determine inputs may be entered in the uncertainty node of the appropriate BDN model (block 4006).

Additionally, inputs for a decision node of a section of a specific BDN model may be determined (block 4008). Here again, the inputs may be determined from the expert data 4004. As described above, in some embodiments, the expert data 4004 may be used to generate probability data stored in a database. The determined inputs and associated probability states may then be entered into a decision node of the appropriate BDN model. (block 4010).

Finally the consequence probabilities may be determined based on the Bayesian logic described above in Equations 1, 2, and 4 (block 4012). Here again, the determination of various probabilities may be determined from expert data 4004. For example, various combinations of inputs to the uncertainty node and decision node may result in different probability states as determined from the expert data 4004. The consequence probabilities may then be entered into the consequences node of the appropriate BDN model (block 4014). Next the section of the BDN model may be completed and additional sections may be constructed in the manner described above.

In some embodiments, after completing a section of a BDN model or all sections of a BDN model, the BDN model may be tested (block 4016). For example, inputs to the uncertainty nodes of the BDN model may be selected and the outputs may be tested against manual determinations based on the expert data 4004. Finally, if the model is complete and tested, the UBD expert system incorporating the BDN model may be provided (block 4018).

Advantageously, in the case of new and changed practices, expert opinions, and the like, a BDN model may be updated by changing the probability states for the appropriate nodes. For example, practices, expert opinions, and the like may be reviewed to determine if there are changes (decision block 4020). If there are new or changed practices, expert opinions, or other sources of expert data (line 4022), then additional expert data may be obtained (block 4024) and used to determine inputs to the uncertainty node and decision node of the appropriate section of a BDN model. Any new and changed determinations may be entered into the appropriate nodes and an updated BDN model may be completed (block 4026).

FIG. 41 depicts a computer 4100 in accordance with an embodiment of the present invention. Various portions or sections of systems and methods described herein include or are executed on one or more computers similar to computer 4100 and programmed as special-purpose machines executing some or all steps of methods described above as executable computer code. Further, processes and modules described herein may be executed by one or more processing systems similar to that of computer 4100. For example, the UBD expert system 108 described may be implemented on one or more computers similar to computer 4100 and programmed to execute one or more of the various Bayesian decision models described above.

As will be understood by those skilled in the art, the computer 4100 may include various internal and external components that contribute to the function of the device and which may allow the computer 4100 to function in accordance with the techniques discussed herein. As will be appreciated, various components of computer 4100 may be provided as internal or integral components of the computer 4100 or may be provided as external or connectable components. It should further be noted that FIG. 41 depicts merely one example of a particular implementation and is intended to illustrate the types of components and functionalities that may be present in computer 4100. As shown in FIG. 41, the computer 4100 may include one or more processors (e.g., processors 4102 a-4102 n) coupled to a memory 4104, a display 4106, I/O ports 4108 and a network interface 4110, via an interface 4114.

Computer 4100 may include any combination of devices or software that may perform or otherwise provide for the performance of the techniques described herein. For example, the computer 4100 may be representative of the client computer 200 or a server implementing some or all portions of the UBD expert system 108 or other components of the systems described above. Accordingly, the computer 4100 may include or be a combination of a cloud-computing system, a data center, a server rack or other server enclosure, a server, a virtual server, a desktop computer, a laptop computer, a tablet computer, a mobile telephone, a personal digital assistant (PDA), a media player, a game console, a vehicle-mounted computer, or the like. The computer 4100 may be a unified device providing any one of or a combination of the functionality of a media player, a cellular phone, a personal data organizer, a game console, and so forth. Computer 4100 may also be connected to other devices that are not illustrated, or may operate as a stand-alone system. In addition, the functionality provided by the illustrated components may in some embodiments be combined in fewer components or distributed in additional components. Similarly, in some embodiments, the functionality of some of the illustrated components may not be provided or other additional functionality may be available.

In addition, the computer 4100 may allow a user to connect to and communicate through a network 4116 (e.g., the Internet, a local area network, a wide area network, etc.) and to acquire data from a satellite-based positioning system (e.g., GPS). For example, the computer 4100 may allow a user to communicate using the World Wide Web (WWW), e-mail, text messaging, instant messaging, or using other forms of electronic communication, and may allow a user to obtain the location of the device from the satellite-based positioning system, such as the location on an interactive map.

In one embodiment, the display 4106 may include a liquid crystal display (LCD) or an organic light emitting diode (OLED) display, although other display technologies may be used in other embodiments. The display 4106 may display a user interface (e.g., a graphical user interface), such a user interface for a Bayesian decision network. In accordance with some embodiments, the display 4106 may include or be provided in conjunction with touch sensitive elements through which a user may interact with the user interface. Such a touch-sensitive display may be referred to as a “touch screen” and may also be known as or called a touch-sensitive display system.

The processor 4102 may provide the processing capability required to execute the operating system, programs, user interface, and any functions of the computer 4100. The processor 4102 may receive instructions and data from a memory (e.g., system memory 4104). The processor 4102 may include one or more processors, such as “general-purpose” microprocessors, and special purpose microprocessors, such as ASICs. For example, the processor 4102 may include one or more reduced instruction set (RISC) processors, such as those implementing the Advanced RISC Machine (ARM) instruction set. Additionally, the processor 4102 may include single-core processors and multicore processors and may include graphics processors, video processors, and related chip sets. Accordingly, computer 4100 may be a uni-processor system including one processor (e.g., processor 4102 a), or a multi-processor system including any number of suitable processors (e.g., 4102 a-4102 n). Multiple processors may be employed to provide for parallel or sequential execution of one or more sections of the techniques described herein. Processes, such as logic flows, described herein may be performed by one or more programmable processors executing one or more computer programs to perform functions by operating on input data and generating corresponding output.

As will be understood by those skilled in the art, the memory 4104 (which may include one or more tangible non-transitory computer readable storage medium) may include volatile memory, such as random access memory (RAM), and non-volatile memory, such as ROM, flash memory, a hard drive, any other suitable optical, magnetic, or solid-state storage medium, or a combination thereof. The memory 4104 may be accessible by the processor 4102 and other components of the computer 4100. The memory 4104 may store a variety of information and may be used for a variety of purposes. The memory 4104 may store executable computer code, such as the firmware for the computer 4100, an operating system for the computer 4100, and any other programs or other executable code necessary for the computer 4100 to function. The executable computer code may include program instructions 4118 executable by a processor (e.g., one or more of processors 4102 a-4102 n) to implement one or more embodiments of the present invention. Instructions 4118 may include modules of computer program instructions for implementing one or more techniques described. Program instructions 4118 may define a computer program (which in certain forms is known as a program, software, software application, script, or code). A computer program may be written in a programming language, including compiled or interpreted languages, or declarative or procedural languages. A computer program may include a unit suitable for use in a computing environment, including as a stand-alone program, a module, a component, a subroutine. A computer program may or may not correspond to a file in a file system. A program may be stored in a section of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or sections of code). A computer program may be deployed to be executed on one or more computer processors located locally at one site or distributed across multiple remote sites and interconnected by a communication network. In addition, the memory 4104 may be used for buffering or caching during operation of the computer 4100. The memory 4104 may also store data files such as media (e.g., music and video files), software (e.g., for implementing functions on computer 4100), preference information (e.g., media playback preferences), wireless connection information (e.g., information that may enable media device to establish a wireless connection), telephone information (e.g., telephone numbers), and any other suitable data.

As mentioned above, the memory 4104 may include volatile memory, such as random access memory (RAM). The memory 4104 may also include non-volatile memory, such as ROM, flash memory, a hard drive, any other suitable optical, magnetic, or solid-state storage medium, or a combination thereof. The interface 4114 may include multiple interfaces and may couple various components of the computer 4100 to the processor 4102 and memory 4104. In some embodiments, the interface 4114, the processor 4102, memory 4104, and one or more other components of the computer 4100 may be implemented on a single chip, such as a system-on-a-chip (SOC). In other embodiments, these components, their functionalities, or both may be implemented on separate chips. The interface 4114 may be configured to coordinate I/O traffic between processors 4102 a-4102 n, system memory 4104, network interface 1410, I/O devices 1412, other peripheral devices, or a combination thereof. The interface 4114 may perform protocol, timing or other data transformations to convert data signals from one component (e.g., system memory 4104) into a format suitable for use by another component (e.g., processors 4102 a-4102 n). The interface 4114 may include support for devices attached through various types of peripheral buses, such as a variant of the Peripheral Component Interconnect (PCI) bus standard or the Universal Serial Bus (USB) standard.

The computer 4100 may also include an input and output port 4108 to allow connection of additional devices, such as I/O devices 4112. Embodiments of the present invention may include any number of input and output ports 4108, including headphone and headset jacks, universal serial bus (USB) ports, Firewire or IEEE-1394 ports, and AC and DC power connectors. Further, the computer 4100 may use the input and output ports to connect to and send or receive data with any other device, such as other portable computers, personal computers, printers, etc.

The computer 4100 depicted in FIG. 41 also includes a network interface 4110, such as a wired network interface card (NIC), wireless (e.g., radio frequency) receivers, etc. For example, the network interface 4110 may receive and send electromagnetic signals and communicate with communications networks and other communications devices via the electromagnetic signals. The network interface 4110 may include known circuitry for performing these functions, including an antenna system, an RF transceiver, one or more amplifiers, a tuner, one or more oscillators, a digital signal processor, a CODEC chipset, a subscriber identity module (SIM) card, memory, and so forth. The network interface 1410 may communicate with networks (e.g., network 4116), such as the Internet, an intranet, a cellular telephone network, a wireless local area network (LAN), a metropolitan area network (MAN), or other devices by wireless communication. The communication may use any suitable communications standard, protocol and technology, including Ethernet, Global System for Mobile Communications (GSM), Enhanced Data GSM Environment (EDGE), a 3G network (e.g., based upon the IMT-2000 standard), high-speed downlink packet access (HSDPA), wideband code division multiple access (W-CDMA), code division multiple access (CDMA), time division multiple access (TDMA), a 4G network (e.g., IMT Advanced, Long-Term Evolution Advanced (LTE Advanced), etc.), Bluetooth, Wireless Fidelity (Wi-Fi) (e.g., IEEE 802.11a, IEEE 802.11b, IEEE 802.11g or IEEE 802.11n), voice over Internet Protocol (VoIP), Wi-MAX, a protocol for email (e.g., Internet message access protocol (IMAP), or any other suitable communication protocol.

Various embodiments may further include receiving, sending or storing instructions and/or data implemented in accordance with the foregoing description upon a computer-accessible medium. Generally speaking, a computer-accessible/readable storage medium may include a non-transitory storage media such as magnetic or optical media, (e.g., disk or DVD/CD-ROM), volatile or non-volatile media such as RAM (e.g. SDRAM, DDR, RDRAM, SRAM, etc.), ROM, etc., as well as transmission media or signals such as electrical, electromagnetic, or digital signals, conveyed via a communication medium such as network and/or a wireless link.

Further modifications and alternative embodiments of various aspects of the invention will be apparent to those skilled in the art in view of this description. Accordingly, this description is to be construed as illustrative only and is for the purpose of teaching those skilled in the art the general manner of carrying out the invention. It is to be understood that the forms of the invention shown and described herein are to be taken as examples of embodiments. Elements and materials may be substituted for those illustrated and described herein, parts and processes may be reversed or omitted, and certain features of the invention may be utilized independently, all as would be apparent to one skilled in the art after having the benefit of this description of the invention. Changes may be made in the elements described herein without departing from the spirit and scope of the invention as described in the following claims. Headings used herein are for organizational purposes only and are not meant to be used to limit the scope of the description.

As used throughout this application, the word “may” is used in a permissive sense (i.e., meaning having the potential to), rather than the mandatory sense (i.e., meaning must). The words “include”, “including”, and “includes” mean including, but not limited to. As used throughout this application, the singular forms “a”, “an” and “the” include plural referents unless the content clearly indicates otherwise. Thus, for example, reference to “an element” includes a combination of two or more elements. Unless specifically stated otherwise, as apparent from the discussion, it is appreciated that throughout this specification discussions utilizing terms such as “processing”, “computing”, “calculating”, “determining” or the like refer to actions or processes of a specific apparatus, such as a special purpose computer or a similar special purpose electronic processing/computing device. In the context of this specification, a special purpose computer or a similar special purpose electronic processing/computing device is capable of manipulating or transforming signals, typically represented as physical electronic or magnetic quantities within memories, registers, or other information storage devices, transmission devices, or display devices of the special purpose computer or similar special purpose electronic processing/computing device. 

What is claimed is:
 1. A system, comprising: one or more processors; a non-transitory tangible computer-readable memory, the memory comprising: an underbalanced drilling expert system executable by the one or more processors and configured to provide one or more underbalanced drilling recommendations based on one or more inputs, the underbalanced drilling expert system comprising an underbalanced drilling Bayesian decision network (BDN) model, the underbalanced drilling BDN model comprising: a first section, comprising: a formation indicators uncertainty node configured to receive one or more formation indicators from the one or more inputs; a formation considerations decision node configured to receive one or more formation considerations from the one or more inputs; and a first consequences node dependent on the formation indicators uncertainty node and the formation considerations decision node and configured to output the one or more underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from one or more formation indicators and the one or more formation considerations; a second section, comprising: a planning phases uncertainty node configured to receive one or more planning phases from the one or more inputs; a planning phases recommendations decision node configured to receive one or more planning phases recommendations from the one or more inputs; and a second consequences node dependent on the planning phases uncertainty node and the planning phases recommendations decision node and configured to output the one or more underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from one or more planning phases and the one or more planning phases recommendations; and a third section, comprising: an equipment requirements uncertainty node configured to receive one or more equipment requirements from the one or more inputs; an equipment recommendations decision node configured to receive one or more equipment recommendations from the one or more inputs; and a third consequences node dependent on the equipment requirements uncertainty node and the equipment recommendations decision node and configured to output the one or more underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more equipment requirements and the one or more equipment recommendations.
 2. The system of claim 1, wherein the UBD BDN model comprises a final consequences node dependent on the first consequences node, the second consequences, and the third consequences node.
 3. The system of claim 1, comprising a user interface configured to display the UBD BDN model and receive user selections of the one or more inputs.
 4. The system of claim 1, wherein the one or more formation indicators, the one or more planning phases, and the one or more equipment requirements are each associated with a respective plurality of probabilities.
 5. A computer-implemented method for an underbalanced drilling expert system having an underbalanced drilling Bayesian decision network (BDN) model, the method comprising: receiving one or more inputs; providing the one or more nodes of a first section of the underbalanced drilling BDN model, the one or more nodes comprising: a formation indicators uncertainty node; a formation considerations decision node; determining one or more underbalanced drilling recommendations at a consequences node of the first section of the underbalanced drilling BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs; providing the one or more underbalanced drilling recommendations to a user.
 6. The method of claim 5, wherein providing the one or more underbalanced drilling recommendations to a user comprises displaying the one or more underbalanced drilling recommendations in a user interface element of a user interface configured to display the UBD BDN model.
 7. The computer-implemented method of claim 5, comprising: providing the one or more inputs to one or more nodes of a second section of the underbalanced drilling BDN model, the one or more nodes comprising: a planning phases uncertainty node configured to receive one or more planning phases; a planning phases recommendations decision node configured to receive one or more planning phases recommendations; determining the one or more underbalanced drilling recommendations at a second consequences node of the second section of the underbalanced drilling BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs.
 8. The computer-implemented method of claim 7, comprising: providing the one or more inputs to one or more nodes of a third section of the underbalanced drilling BDN model, the one or more nodes comprising: an equipment requirements uncertainty node configured to receive one or more equipment requirements; an equipment recommendations decision node configured to receive one or more equipment recommendations; determining the one or more underbalanced drilling recommendations at a third consequences node of the third section of the underbalanced drilling BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs.
 9. A system, comprising: one or more processors; a non-transitory tangible computer-readable memory, the memory comprising: an underbalanced drilling expert system executable by the one or more processors and configured to provide one or more flow underbalanced drilling recommendations based on one or more inputs, the flow underbalanced drilling expert system comprising a flow underbalanced drilling Bayesian decision network (BDN) model, the flow underbalanced drilling BDN model comprising: a first section, comprising: a tripping types uncertainty node configured to receive one or more tripping types from the one or more inputs; a permeability level uncertainty node configured to receive one or more permeability levels from the one or more inputs; a tripping options decision node configured to receive one or more tripping options from the one or more inputs; a first consequences node dependent on the tripping uncertainty node, the permeability level uncertainty node, and the tripping options decision node and configured to output the one or more flow underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more tripping types, the one or more permeability levels, and the one or more tripping options; a second section, comprising: a connection types uncertainty node configured to receive one or more connection types from the one or more inputs; a connection options decision node configured to receive one or more connection options from the one or more inputs; a second consequences node dependent on the connection uncertainty node and the connection options decision node and configured to output the one or more flow underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more connection types and the one or more connection options; a third section, comprising: a flow drilling types uncertainty node configured to receive one or more flow drilling types from the one or more inputs; a flow drilling options decision node configured to receive one or more flow drilling options from the one or more inputs; a third consequences node dependent on the flow drilling uncertainty node and the flow drilling options decision node and configured to output the one or more flow underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more flow drilling types and the one or more flow drilling options.
 10. The system of claim 9, wherein the flow UBD BDN model comprises a final consequences node dependent on the first consequences node, the second consequences, and the third consequences node.
 11. The system of claim 9, comprising a user interface configured to display the flow UBD BDN model and receive user selections of the one or more inputs.
 12. The system of claim 9, wherein the one or more tripping types, the one or more permeability levels, the one or connection types, and the one or more flow drilling types are each associated with a respective plurality of probabilities.
 13. A computer-implemented method for an underbalanced drilling expert system having a flow underbalanced drilling (UBD) Bayesian decision network (BDN) model, the method comprising: receiving one or more inputs; providing the one or more inputs to one or more nodes of a first section of the flow underbalanced drilling BDN model, the one or more nodes comprising: a tripping uncertainty node configured to receive one or more tripping types; a permeability level uncertainty node configured to receive one or more permeability levels; and a tripping options decision node a tripping options decision node configured to receive one or more tripping options; determining one or more underbalanced drilling recommendations at a consequences node of the first section of the flow underbalanced drilling BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs; providing the one or more underbalanced drilling recommendations to a user.
 14. The computer-implemented method of claim 13, wherein providing the one or more underbalanced drilling recommendations to a user comprises displaying the one or more underbalanced drilling recommendations in a user interface element of a user interface configured to display the flow UBD BDN model.
 15. The computer-implemented method of claim 13, comprising: providing the one or more inputs to one or more nodes of a second section of the flow UBD BDN model, the one or more nodes comprising: a connection types uncertainty node configured to receive one or more connection types; a connection options decision node configured to receive one or more connection options; determining the one or more underbalanced drilling recommendations at a second consequences node of the second section of the underbalanced drilling BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs.
 16. The computer-implemented method of claim 15, comprising: providing the one or more inputs to one or more nodes of a third section of the flow UBD BDN model, the one or more nodes comprising: a flow drilling types uncertainty node configured to receive one or more flow drilling types; a flow drilling options decision node configured to receive one or more flow drilling options; determining the one or more underbalanced drilling recommendations at a third consequences node of the third section of the flow UBD BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs.
 17. A system, comprising: one or more processors; a non-transitory tangible computer-readable memory accessible by the one or more processors, the memory comprising: an underbalanced drilling expert system executable by the one or more processors and configured to provide one or more underbalanced drilling recommendations based on one or more inputs, the underbalanced drilling expert system comprising a gaseated underbalanced drilling Bayesian decision network (BDN) model, the gaseated underbalanced drilling BDN model comprising: a first section, comprising: a gas injection process uncertainty node configured to receive one or more gas injection process types from the one or more inputs; a gas injection processes characteristics decision node configured to receive one or more gas injection process characteristics from the one or more inputs; a first consequences node dependent on the gas injection process uncertainty node and the gas infection processes considerations decision node and configured to output the one or more gaseated underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more gas injection process types and the one or more gas injection process characteristics; a second section, comprising: a fluid volume limits uncertainty node configured to receive one or more fluid volume limits from the one or more inputs; a fluid volume limits requirements decision node configured to receive one or more fluid volume limits requirements from the one or more inputs; a second consequences node dependent on the fluid volume limits uncertainty node and the fluid volume limits requirements decision node and configured to output the one or more gaseated underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more fluid volume limits and the one or more fluid volume limits requirements; a third section, comprising: a kick type uncertainty node configured to receive one or more kick types from the one or more inputs; a kicks recommendations decision node configured to receive one or more kicks recommendations from the one or more inputs; a third consequences node dependent on the kick type uncertainty node and the kicks recommendations decision node and configured to output the one or more gaseated underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more kick types and the one or more kicks recommendations; and a fourth section, comprising: an operational considerations uncertainty node configured to receive one or more operational considerations from the one or more inputs; an operational recommendations decision node configured to receive one or more operational recommendations from the one or more inputs; and a fourth consequences node dependent on the operational considerations uncertainty node and the operational recommendations decision node and configured to output the one or more gaseated underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more operational recommendations and the one or more operational recommendations.
 18. The system of claim 17, wherein the gaseated UBD BDN model comprises a final consequences node dependent on the first consequences node, the second consequences, the third consequences node, and the fourth consequences node.
 19. The system of claim 17, comprising a user interface configured to display the gaseated UBD BDN model and receive user selections of the one or more inputs.
 20. The system of claim 17, wherein the one or more gas injection process types, the one or more fluid volume limits, the one or kick types, and the one or more operational considerations are each associated with a respective plurality of probabilities
 21. A computer-implemented method for an underbalanced drilling expert system having a gaseated underbalanced drilling Bayesian decision network (BDN) model, the method comprising: receiving one or more inputs; providing the one or more inputs to one or more nodes of a first section of the gaseated underbalanced drilling (UBD) BDN model, the one or more nodes comprising: a gas injection process uncertainty node configured to receive one or more gas injection process types; a gas injection processes characteristics decision node configured to receive one or more gas injection process characteristics; determining one or more underbalanced drilling recommendations at a consequences node of the first section of the gaseated UBD BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs; providing the one or more underbalanced drilling recommendations to a user.
 22. The computer-implemented method of claim 21, wherein providing the one or more underbalanced drilling recommendations to a user comprises displaying the one or more underbalanced drilling recommendations in a user interface element of a user interface configured to display the gaseated UBD BDN model.
 23. The computer-implemented method of claim 21, comprising: providing the one or more inputs to one or more nodes of a second section of the gaseated UBD BDN model, the one or more nodes comprising: a fluid volume limits uncertainty node configured to receive one or more fluid volume limits from the one or more inputs; a fluid volume limits requirements decision node configured to receive one or more fluid volume limits requirements; determining the one or more underbalanced drilling recommendations at a second consequences node of the second section of the gaseated UBD BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs.
 24. The computer-implemented method of claim 23, comprising: providing the one or more inputs to one or more nodes of a third section of the gaseated UBD BDN model, the one or more nodes comprising: a kick type uncertainty node configured to receive one or more kick types; a kicks recommendations decision node configured to receive one or more kicks recommendations; determining the one or more underbalanced drilling recommendations at a third consequences node of the third section of the gaseated UBD BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs.
 25. The computer-implemented method of claim 24, comprising: providing the one or more inputs to one or more nodes of a fourth section of the gaseated UBD BDN model, the one or more nodes comprising: an operational considerations uncertainty node configured to receive one or more operational considerations; an operational recommendations decision node configured to receive one or more operational recommendations; determining the one or more underbalanced drilling recommendations at a fourth consequences node of the third section of the gaseated UBD BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs.
 26. A system, comprising: one or more processors; a non-transitory tangible computer-readable memory accessible by the one or more processors, the memory comprising: an underbalanced drilling expert system executable by the one or more processors and configured to provide one or more underbalanced drilling recommendations based on one or more inputs, the underbalanced drilling expert system comprising a foam underbalanced drilling (UBD) Bayesian decision network (BDN) model, the foam UBD BDN model comprising: a first section, comprising: a foam systems considerations uncertainty node configured to receive one or more foam systems considerations from the one or more inputs; a foam systems recommendations decision node configured to receive one or more foam systems recommendations from the one or more inputs; and a first consequences node dependent on the foam systems considerations uncertainty node and the foam systems recommendations decision node and configured to output the one or more underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more foam systems considerations and the one or more foam systems recommendations; and a second section, comprising: a foam systems designs uncertainty node configured to receive one or more foam system designs from the one or more inputs; a foam system designs recommendations decision node configured to receive one or more foam system designs recommendations from the one or more inputs; and a second consequences node dependent on the foam systems designs uncertainty node and the foam system designs recommendations decision node and configured to output the one or more underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more foam system designs and the one or more foam system designs recommendations.
 27. The system of claim 26, wherein the foam UBD BDN model comprises a final consequences node dependent on the first consequences node and the second consequences node.
 28. The system of claim 26, comprising a user interface configured to display the foam UBD BDN model and receive user selections of the one or more inputs.
 29. The system of claim 26, wherein the one or more foam systems considerations and the one or more foam systems designs are each associated with a respective plurality of probabilities.
 30. A computer-implemented method for an underbalanced drilling expert system having a foam underbalanced drilling (UBD) Bayesian decision network (BDN) model, the method comprising: receiving one or more inputs; providing the one or more inputs to one or more nodes of a first section of the foam UBD BDN model, the one or more nodes comprising: a foam systems considerations uncertainty node configured to receive one or more foam systems considerations; and a foam systems recommendations decision node configured to receive one or more foam systems recommendations; determining one or more underbalanced drilling recommendations at a consequences node of the first section of the foam UBD BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs; and providing the one or more underbalanced drilling recommendations to a user.
 31. The computer-implemented method of claim 30, wherein providing the one or more underbalanced drilling recommendations to a user comprises displaying the one or more underbalanced drilling recommendations in a user interface element of a user interface configured to display the foam UBD BDN model.
 32. The computer-implemented method of claim 30, comprising: providing the one or more inputs to one or more nodes of a second section of the foam UBD BDN model, the one or more nodes comprising: a foam systems designs uncertainty node configured to receive one or more foam system designs; a foam system designs recommendations decision node configured to receive one or more foam system designs recommendations; determining the one or more underbalanced drilling recommendations at a second consequences node of the second section of the foam UBD BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs.
 33. A system, comprising: one or more processors; a non-transitory tangible computer-readable memory, the memory comprising: an underbalanced drilling expert system executable by the one or more processors and configured to provide one or more underbalanced drilling recommendations based on one or more inputs, the underbalanced drilling expert system comprising a gas underbalanced drilling (UBD) Bayesian decision network (BDN) model, the gas underbalanced drilling BDN model comprising: a first section, comprising: a rotary and hammer drilling uncertainty node configured to receive one or more rotary and hammer drilling types from the one or more inputs; a rotary and hammer drilling recommendations decision node configured to receive one or more rotary and hammer drilling recommendations from the one or more inputs; and a first consequences node dependent on the rotary and hammer drilling uncertainty node and the rotary and hammer drilling recommendations decision node and configured to output the one or more air and gas underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more rotary and hammer drilling types and the one or more rotary and hammer drilling recommendations; a second section, comprising: a gas drilling considerations uncertainty node configured to receive one or more gas drilling considerations from the one or more inputs; a gas drilling considerations recommendations decision node configured to receive gas drilling considerations recommendations from the one or more inputs; and a second consequences node dependent on the gas drilling considerations uncertainty node and the gas drilling considerations recommendations decision node and configured to output the one or more air and gas underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more gas drilling considerations and the one or more gas drilling considerations recommendations; a third section, comprising: a gas drilling operations uncertainty node configured to receive one or more gas drilling operations from the one or more inputs; a gas drilling operations recommendations decision node configured to receive gas drilling operations recommendations from the one or more inputs; and a third consequences node dependent on the gas drilling operations uncertainty node and the gas drilling operations recommendations decision node and configured to output the one or more air and gas underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more gas drilling operations and the one or more gas drilling operations recommendations; and a fourth section, comprising: a gas drilling rig equipment uncertainty node configured to receive one or more gas drilling rig equipment from the one or more inputs; a gas drilling rig equipment recommendations decision node configured to receive gas drilling rig equipment recommendations from the one or more inputs; and a fourth consequences node dependent on the gas drilling rig equipment uncertainty node and the gas drilling rig equipment recommendations decision node and configured to output the one or more air and gas underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more gas drilling rig equipment and the one or more gas drilling rig equipment recommendations.
 34. The system of claim 33, wherein the gas UBD BDN model comprises a final consequences node dependent on the first consequences node, the second consequences node, the third consequences node, and the fourth consequences node.
 35. The system of claim 33, comprising a user interface configured to display the gas UBD BDN model and receive user selections of the one or more inputs.
 36. The system of claim 33, wherein the one or more rotary and hammer drilling types, the one or more gas drilling considerations, the one or more gas drilling operations, and the one or more gas drilling rig equipment are each associated with a respective plurality of probabilities.
 37. A computer-implemented method for an underbalanced drilling expert system having a gas underbalanced drilling (UBD) Bayesian decision network (BDN) model, the method comprising: receiving one or more inputs; providing the one or more inputs to one or more nodes of a first section of the gas underbalanced drilling BDN model, the one or more nodes comprising: a rotary and hammer drilling uncertainty node; a rotary and hammer recommendations decision node; determining one or more underbalanced drilling recommendations at a consequences node of the first section of the gas underbalanced drilling BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs; providing the one or more underbalanced drilling recommendations to a user.
 38. The computer-implemented method of claim 37, wherein providing the one or more underbalanced drilling recommendations to a user comprises displaying the one or more underbalanced drilling recommendations in a user interface element of a user interface configured to display the gas UBD BDN model.
 39. The computer-implemented method of claim 37, comprising: providing the one or more inputs to one or more nodes of a second section of the gas UBD BDN model, the one or more nodes comprising: a gas drilling considerations uncertainty node configured to receive one or more gas drilling considerations; a gas drilling considerations recommendations decision node configured to receive gas drilling considerations recommendations; determining the one or more underbalanced drilling recommendations at a second consequences node of the second section of the gas UBD BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs.
 40. The computer-implemented method of claim 39, comprising: providing the one or more inputs to one or more nodes of a third section of the gas UBD BDN model, the one or more nodes comprising: a gas drilling operations uncertainty node configured to receive one or more gas drilling operations; a gas drilling operations recommendations decision node configured to receive gas drilling operations recommendations; determining the one or more underbalanced drilling recommendations at a second consequences node of the third section of the gas UBD BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs.
 41. The computer-implemented method of claim 40, comprising: providing the one or more inputs to one or more nodes of a fourth section of the gas UBD BDN model, the one or more nodes comprising: a gas drilling rig equipment uncertainty node configured to receive one or more gas drilling rig equipment from the one or more inputs; a gas drilling rig equipment recommendations decision node configured to receive gas drilling rig equipment recommendations; determining the one or more underbalanced drilling recommendations at a fourth consequences node of the fourth section of the gas UBD BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs.
 42. A system, comprising, one or more processors; a non-transitory tangible computer-readable memory, the memory comprising: a mud cap underbalanced drilling expert system executable by the one or more processors and configured to provide one or more mud cap underbalanced drilling recommendations based on one or more inputs, the mud cap underbalanced drilling expert system comprising a mud cap underbalanced drilling Bayesian decision network (BDN) model, the mud cap underbalanced drilling BDN model comprising: a first section, comprising: a mud cap drilling types uncertainty node configured to receive one or more mud cap drilling types from the one or more inputs; a mud cap drilling types recommendations decision node configured to receive one or more mud cap drilling types recommendations from the one or more inputs; and a first consequences node dependent on the mud cap drilling types uncertainty node and the mud cap drilling types recommendations decision node and configured to output the one or more mud cap underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more mud cap drilling types and the one or more mud cap drilling types recommendations; a second section, comprising: a mud cap drilling problems uncertainty node configured to receive one or more mud cap drilling problems from the one or more inputs; a mud cap drilling problems recommendations decision node configured to receive one or more mud cap drilling problems recommendations from the one or more inputs; and a second consequences node dependent on the mud cap drilling problems uncertainty node and the mud cap drilling problems recommendations decision node and configured to output the one or more mud cap underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more mud cap drilling problems and the one or more mud cap drilling problems recommendations; and a third section, comprising: a floating mud cap drilling considerations uncertainty node configured to receive one or more floating mud cap drilling considerations types from the one or more inputs; a floating mud cap drilling recommendations decision node configured to receive one or more floating mud cap drilling recommendations from the one or more inputs; and a third consequences node dependent on the floating mud cap drilling considerations uncertainty node and the floating mud cap drilling recommendations decision node and configured to output the one or more mud cap underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more floating mud cap drilling considerations types and the one or more floating mud cap drilling recommendations.
 43. The system of claim 42, wherein the mud cap UBD BDN model comprises a final consequences node dependent on the first consequences node, the second consequences node, and the third consequences node.
 44. The system of claim 42, comprising a user interface configured to display the mud cap UBD BDN model and receive user selections of the one or more inputs.
 45. The system of claim 42, wherein the one or more mud cap drilling types, the one or more mud cap drilling problems, and the one or more floating mud cap considerations are each associated with a respective plurality of probabilities.
 46. A computer-implemented method for an underbalanced drilling expert system having a mud cap underbalanced drilling (UBD) Bayesian decision network (BDN) model, the method comprising: receiving one or more inputs; providing the one or more inputs to one or more nodes of a first section of the mud cap UBD BDN model, the one or more nodes comprising: a mud cap drilling types uncertainty node configured to receive one or more mud cap drilling types; a mud cap drilling types recommendations decision node configured to receive one or more mud cap drilling types recommendations; determining one or more underbalanced drilling recommendations at a consequences node of the first section of the mud cap UBD BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs; and providing the one or more underbalanced drilling recommendations to a user.
 47. The computer-implemented method of claim 46, wherein providing the one or more underbalanced drilling recommendations to a user comprises displaying the one or more underbalanced drilling recommendations in a user interface element of a user interface configured to display the mud cap UBD BDN model.
 48. The computer-implemented method of claim 46, comprising: providing the one or more inputs to one or more nodes of a second section of the mud cap UBD BDN model, the one or more nodes comprising: a mud cap drilling problems uncertainty node configured to receive one or more mud cap drilling problems; a mud cap drilling problems recommendations decision node configured to receive one or more mud cap drilling problems recommendations; determining the one or more underbalanced drilling recommendations at a second consequences node of the second section of the gas UBD BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs.
 49. The computer-implemented method of claim 48, comprising: providing the one or more inputs to one or more nodes of a third section of the mud cap UBD BDN model, the one or more nodes comprising: a floating mud cap drilling considerations uncertainty node configured to receive one or more floating mud cap drilling considerations; a floating mud cap drilling recommendations decision node configured to receive one or more floating mud cap drilling recommendations; determining the one or more underbalanced drilling recommendations at a third consequences node of the third section of the mud cap UBD BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs.
 50. A system, comprising, one or more processors; a non-transitory tangible computer-readable memory, the memory comprising: a underbalanced drilling expert system executable by the one or more processors and configured to provide one or more underbalanced drilling recommendations based on one or more inputs, the underbalanced expert system comprising an underbalanced liner drilling (UBLD) Bayesian decision network (BDN) model, the UBLD BDN model comprising: a first section, comprising: a UBLD plans uncertainty node configured to receive one or more UBLD plans from the one or more inputs; a UBLD plans recommendations decision node configured to receive one or more UBLD plans recommendations from the one or more inputs; and a first consequences node dependent on the UBLD planning uncertainty node and the UBLD planning recommendations decision node and configured to output the one or more underbalanced liner drilling recommendations based on one or more Bayesian probabilities calculated from the one or more UBLD plans and the one or more UBLD plans recommendations; a second section, comprising: a UBLD solvable problems uncertainty node configured to receive one or more UBLD solvable problems from the one or more inputs; a UBLD advantages decision node configured to receive one or more UBLD advantages from the one or more inputs; and a second consequences node dependent on the UBLD problems uncertainty node and the UBLD advantages decision node and configured to output the one or more underbalanced liner drilling recommendations based on one or more Bayesian probabilities calculated from the one or more UBLD solvable problems and the one or more UBLD advantages; and a third section, comprising: a UBLD considerations uncertainty node configured to receive one or more UBLD considerations from the one or more inputs; a UBLD considerations recommendations decision node configured to receive one or more UBLD considerations recommendations from the one or more inputs; and a third consequences node dependent on the UBLD considerations uncertainty node and the UBLD recommendations decision node and configured to output the one or more underbalanced liner drilling recommendations based on one or more Bayesian probabilities calculated from the one or more UBLD considerations and the one or more UBLD considerations recommendations.
 51. The system of claim 50, wherein the UBLD BDN model comprises a final consequences node dependent on the first consequences node, the second consequences node, and the third consequences node.
 52. The system of claim 50, comprising a user interface configured to display the UBLD BDN model and receive user selections of the one or more inputs.
 53. The system of claim 50, wherein the one or more UBLD plans, the one or more UBLD solvable problems, and the one or more UBLD considerations are each associated with a respective plurality of probabilities.
 54. A computer-implemented method for an underbalanced drilling expert system having an underbalanced liner drilling (UBLD) Bayesian decision network (BDN) model, the method comprising: receiving one or more inputs; providing the one or more inputs to one or more nodes of a first section of the UBLD BDN model, the one or more nodes comprising: a UBLD plans uncertainty node configured to receive one or more UBLD plans; a UBLD plans recommendations decision node configured to receive one or more UBLD plans recommendations; determining one or more underbalanced drilling recommendations at a consequences node of the first section of the UBLD BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs; providing the one or more underbalanced drilling recommendations to a user.
 55. The computer-implemented method of claim 54, wherein providing the one or more underbalanced drilling recommendations to a user comprises displaying the one or more underbalanced drilling recommendations in a user interface element of a user interface configured to display the UBLD BDN model.
 56. The computer-implemented method of claim 54, comprising: providing the one or more inputs to one or more nodes of a second section of the UBLD BDN model, the one or more nodes comprising: a UBLD solvable problems uncertainty node configured to receive one or more UBLD solvable problems; a UBLD advantages decision node configured to receive one or more UBLD advantages; determining the one or more underbalanced drilling recommendations at a second consequences node of the second section of the UBLD BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs.
 57. The computer-implemented method of claim 56, comprising: providing the one or more inputs to one or more nodes of a third section of the UBLD BDN model, the one or more nodes comprising: a UBLD considerations uncertainty node configured to receive one or more UBLD considerations; a UBLD considerations recommendations decision node configured to receive one or more UBLD considerations recommendations; determining the one or more underbalanced drilling recommendations at a third consequences node of the third section of the UBLD BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs.
 58. A system, comprising: one or more processors; a non-transitory tangible computer-readable memory, the memory comprising: an underbalanced drilling (UBD) expert system executable by the one or more processors and configured to provide one or more UBD recommendations based on one or more inputs, the UBD expert system comprising an underbalanced coil tube (UBCT) Bayesian decision network (BDN) model, the UBCT BDN model comprising: a first section, comprising: a UBCT preplanning uncertainty node configured to receive one or more UBCT preplans from the one or more inputs; a UBCT preplanning requirements decision node configured to receive one or more UBCT preplan requirements from the one or more inputs; and a first consequences node dependent on the UBCT preplanning uncertainty node and the UBCT preplanning recommendations decision node and configured to output the one or more UBCT drilling requirements based on one or more Bayesian probabilities calculated from the one or more UBCT preplans and the one or more UBCT preplan requirements; and a second section, comprising: a UBCT considerations uncertainty node configured to receive one or more UBCT considerations from the one or more inputs; a UBCT recommendations decision node configured to receive one or more UBCT recommendations from the one or more inputs; and a second consequences node dependent on the UBCT considerations uncertainty node and the UBCT recommendations decision node and configured to output the one or more underbalanced drilling recommendations based on one or more Bayesian probabilities calculated from the one or more UBCT considerations and the one or more UBCT recommendations.
 59. The system of claim 58, wherein the UBCT BDN model comprises a final consequences node dependent on the first consequences node and the second consequences node.
 60. The system of claim 58, comprising a user interface configured to display the UBCT BDN model and receive user selections of the one or more inputs.
 61. The system of claim 58, wherein the one or more UBCT preplans and the one or more UBCT considerations are each associated with a respective plurality of probabilities.
 62. A computer-implemented method for an underbalanced drilling expert system having an underbalanced coil tube (UBCT) drilling Bayesian decision network (BDN) model, the method comprising: receiving one or more inputs; providing the one or more inputs to one or more nodes of a first section of the UBCT BDN model, the one or more nodes comprising: a UBCT preplanning uncertainty node configured to receive one or more UBCT preplans; a UBCT preplanning requirements decision node configured to receive one or more UBCT preplan requirements; determining one or more underbalanced drilling recommendations at a consequences node of the first section of the UBCT BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs; providing the one or more underbalanced drilling recommendations to a user.
 63. The computer-implemented method of claim 62, wherein providing the one or more underbalanced drilling recommendations to a user comprises displaying the one or more underbalanced drilling recommendations in a user interface element of a user interface configured to display the UBCT BDN model.
 64. The computer-implemented method of claim 62, comprising: providing the one or more inputs to one or more nodes of a second section of the UBCT BDN model, the one or more nodes comprising: a UBCT considerations uncertainty node configured to receive one or more UBCT considerations; a UBCT recommendations decision node configured to receive one or more UBCT recommendations; determining the one or more underbalanced drilling recommendations at a second consequences node of the second section of the UBCT BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs.
 65. A system, comprising: one or more processors; a non-transitory tangible computer-readable memory, the memory comprising: an underbalanced drilling expert system executable by the one or more processors and configured to provide one or more underbalanced drilling recommendations based on one or more inputs, the underbalanced drilling expert system comprising a snubbing and stripping Bayesian decision network (BDN) model, the snubbing and stripping BDN model comprising a first section, comprising: a snubbing types uncertainty node configured to receive one or more snubbing types from the one or more inputs; a snubbing types recommendations decision node configured to receive one or more snubbing types recommendations from the one or more inputs; and a first consequences node dependent on the snubbing types uncertainty node and the snubbing types recommendations decision node and configured to output the one or more underbalanced recommendations based on one or more Bayesian probabilities calculated from the one or more snubbing types and the one or more snubbing types recommendations; and a second section, comprising: a snubbing units uncertainty node configured to receive one or more snubbing units from the one or more inputs; a snubbing units recommendations decision node configured to receive one or more snubbing units recommendations from the one or more inputs; and a second consequences node dependent on the snubbing units uncertainty node and the snubbing units recommendations decision node and configured to output the one or more stripping and snubbing recommendations based on one or more Bayesian probabilities calculated from the one or more snubbing units types and the one or more snubbing units recommendations; and a third section, comprising: a snubbing operations uncertainty node configured to receive one or more snubbing operations from the one or more inputs; a snubbing operations recommendations decision node configured to receive one or more snubbing operations recommendations from the one or more inputs; and a third consequences node dependent on the snubbing operations uncertainty node and the snubbing operations recommendations decision node and configured to output the one or more stripping and snubbing recommendations based on one or more Bayesian probabilities calculated from the one or more snubbing operations and the one or more snubbing operations recommendations; and a fourth section, comprising: a stripping procedures uncertainty node configured to receive one or more stripping procedures from the one or more inputs; a stripping procedures recommendations decision node configured to receive one or more stripping procedures recommendations from the one or more inputs; and a fourth consequences node dependent on the stripping procedures uncertainty node and the stripping procedures recommendations decision node and configured to output the one or more stripping and snubbing recommendations based on one or more Bayesian probabilities calculated from the one or more stripping procedures and the one or more stripping procedures recommendations.
 66. The system of claim 65, wherein the snubbing and stripping BDN model comprises a final consequences node dependent on the first consequences node and the second consequences node.
 67. The system of claim 65, comprising a user interface configured to display the snubbing and stripping BDN model and receive user selections of the one or more inputs.
 68. The system of claim 65, wherein the one or more snubbing types, the one or more snubbing units, the one or more snubbing operations, and the one or more stripping procedures are each associated with a respective plurality of probabilities.
 69. A computer-implemented method for an underbalanced drilling expert system having a snubbing and stripping Bayesian decision network (BDN) model, the method comprising: receiving one or more inputs; providing the one or more inputs to one or more nodes of a first section of the snubbing and stripping BDN model, the one or more nodes comprising: a snubbing types uncertainty node configured to receive one or more snubbing types; a snubbing types recommendations decision node configured to receive one or more snubbing types recommendations; determining one or more underbalanced drilling recommendations at a consequences node of the first section of the snubbing and stripping BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs; and providing the one or more underbalanced drilling recommendations to a user.
 70. The computer-implemented method of claim 69, wherein providing the one or more underbalanced drilling recommendations to a user comprises displaying the one or more underbalanced drilling recommendations in a user interface element of a user interface configured to display the snubbing and stripping BDN model.
 71. The computer-implemented method of claim 69, comprising: providing the one or more inputs to one or more nodes of a second section of the snubbing and stripping BDN model, the one or more nodes comprising: a snubbing units uncertainty node configured to receive one or more snubbing units; a snubbing units recommendations decision node configured to receive one or more snubbing units recommendations; determining the one or more underbalanced drilling recommendations at a second consequences node of the second section of the snubbing and stripping BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs.
 72. The computer-implemented method of claim 71, comprising: providing the one or more inputs to one or more nodes of a third section of the snubbing and stripping BDN model, the one or more nodes comprising: a snubbing operations uncertainty node configured to receive one or more snubbing operations; a snubbing operations recommendations decision node configured to receive one or more snubbing operations recommendations; determining the one or more underbalanced drilling recommendations at a third consequences node of the third section of the snubbing and stripping BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs.
 73. The computer-implemented method of claim 72, comprising: providing the one or more inputs to one or more nodes of a fourth section of the snubbing and stripping BDN model, the one or more nodes comprising: a stripping procedures uncertainty node configured to receive one or more stripping procedures; a stripping procedures recommendations decision node configured to receive one or more stripping procedures recommendations; determining the one or more underbalanced drilling recommendations at a fourth consequences node of the fourth section of the snubbing and stripping BDN model, the determination comprising a calculation of one or more Bayesian probabilities based on the one or more inputs. 